Mathematische Nachrichten最新文献

{"title":"Homogeneous Einstein and Einstein–Randers metrics on Stiefel manifolds","authors":"Marina Statha","doi":"10.1002/mana.70009","DOIUrl":"https://doi.org/10.1002/mana.70009","url":null,"abstract":"<p>We study invariant Einstein metrics and Einstein–Randers metrics on the Stiefel manifold <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mi>k</mi>\u0000 </msub>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mo>=</mo>\u0000 <mi>SO</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>/</mo>\u0000 <mi>SO</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mi>k</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$V_kmathbb {R}^n={mathsf {SO}}(n)/{mathsf {SO}}(n-k)$</annotation>\u0000 </semantics></math>. We use a characterization for (nonflat) homogeneous Einstein–Randers metrics as pairs of (nonflat) homogeneous Einstein metrics and invariant Killing vector fields. It is well known that, for Stiefel manifolds the isotropy representation contains equivalent summands, so a complete description of invariant metrics is difficult. We prove, by assuming additional symmetries, that the Stiefel manifolds <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>+</mo>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msub>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>+</mo>\u0000 <mn>2</mn>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mspace></mspace>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$V_{1+k}mathbb {R}^{1+2k} (k &gt; 2)$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>V</mi>\u0000 <mn>6</mn>\u0000 </msub>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <mspace></mspace>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>≥</mo>\u0000 <mn>8</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$V_{6}mathbb ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2652-2674"},"PeriodicalIF":0.8,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some inequalities on weighted Sobolev spaces, distance weights, and the Assouad dimension","authors":"Fernando López-García,&nbsp;Ignacio Ojea","doi":"10.1002/mana.70014","DOIUrl":"https://doi.org/10.1002/mana.70014","url":null,"abstract":"&lt;p&gt;We considercertain inequalities and a related result on weighted Sobolev spaces on bounded John domains in &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;${mathbb {R}}^n$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Namely, we study the existence of a right inverse for the divergence operator, along with the corresponding a priori estimate, the improved and the fractional Poincaré inequalities, the Korn inequality, and the local Fefferman–Stein inequality. All these results are obtained on weighted Sobolev spaces, where the weight is a power of the distance to the boundary. In all cases the exponent of the weight &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;β&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$d(cdot,partial Omega)^{beta p}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is only required to satisfy the restriction: &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;β&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;&gt;&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;dim&lt;/mi&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$beta p&gt;-(n-{rm dim}_A(partial Omega))$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the exponent of the Sobolev space and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;dim&lt;/mi&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;Ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm dim}_A(partial Omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the Assouad dimension of the boundary of the domain. To the best of our knowledge, this condition is less restrictive ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2749-2769"},"PeriodicalIF":0.8,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fractional-order trace-dev-div inequality","authors":"C. Carstensen,&nbsp;N. Heuer","doi":"10.1002/mana.70003","DOIUrl":"https://doi.org/10.1002/mana.70003","url":null,"abstract":"<p>The trace-dev-div inequality in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>s</mi>\u0000 </msup>\u0000 <annotation>$H^s$</annotation>\u0000 </semantics></math> controls the trace in the norm of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>s</mi>\u0000 </msup>\u0000 <annotation>$H^s$</annotation>\u0000 </semantics></math> by that of the deviatoric part plus the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$H^{s-1}$</annotation>\u0000 </semantics></math> norm of the divergence of a quadratic tensor field different from the constant unit matrix. This is well known for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$s=0$</annotation>\u0000 </semantics></math> and established for orders <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>≤</mo>\u0000 <mi>s</mi>\u0000 <mo>≤</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$0le sle 1$</annotation>\u0000 </semantics></math> and arbitrary space dimension in this paper. For mixed and least-squares finite element error analysis in linear elasticity, this inequality allows to establish robustness with respect to the Lamé parameter <span></span><math>\u0000 <semantics>\u0000 <mi>λ</mi>\u0000 <annotation>$lambda$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2493-2498"},"PeriodicalIF":0.8,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global strong solution for the two-dimensional magnetohydrodynamics equations with shearing-periodic boundary conditions","authors":"Shintaro Kondo,&nbsp;Tatsuki Nakamura","doi":"10.1002/mana.70012","DOIUrl":"https://doi.org/10.1002/mana.70012","url":null,"abstract":"<p>In this paper, we investigate the two-dimensional (2D), two-field magnetohydrodynamics (MHD) equations in the presence of a shear flow, assuming positive plasma viscosity and resistivity. We establish the global-in-time existence and uniqueness of a strong solution for the 2D two-field MHD equations under shearing-periodic boundary conditions, as proposed by Hawley et al. Moreover, we establish the existence and uniqueness of a strong solution for the linear advection-diffusion equation under shearing-periodic boundary condition by employing uniformly local <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math> spaces.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2712-2739"},"PeriodicalIF":0.8,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Large time behavior for the nonlinear dissipative Boussinesq equation","authors":"Wenhui Chen,&nbsp;Hiroshi Takeda","doi":"10.1002/mana.70015","DOIUrl":"https://doi.org/10.1002/mana.70015","url":null,"abstract":"<p>In this paper, we study the nonlinear dissipative Boussinesq equation in the whole space <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$L^1$</annotation>\u0000 </semantics></math> integrable data. As our preparations, the optimal estimates as well as the optimal leading terms for the linearized model are derived by performing the Wentzel–Kramers–Brillouin (WKB) analysis and the Fourier analysis. Then, under some conditions on the power <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math> of nonlinearity, we demonstrate global (in time) existence of small data Sobolev solutions with different regularities to the nonlinear model by applying some fractional-order interpolations, where the optimal growth (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$n=2$</annotation>\u0000 </semantics></math>) and decay (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 3$</annotation>\u0000 </semantics></math>) estimates of solutions for large time are given. Simultaneously, we get a new large time asymptotic profile of global (in time) solutions. These results imply some influence of dispersion and dissipation on qualitative properties of solution.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2770-2793"},"PeriodicalIF":0.8,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144833212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the completeness of the space \u0000 \u0000 \u0000 O\u0000 C\u0000 \u0000 $mathcal {O}_C$","authors":"Michael Kunzinger,&nbsp;Norbert Ortner","doi":"10.1002/mana.70013","DOIUrl":"https://doi.org/10.1002/mana.70013","url":null,"abstract":"&lt;p&gt;We explicitly prove the compact regularity of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;LF&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathcal {LF}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-space of double sequences &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;lim&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mover&gt;\u0000 &lt;mo&gt;⊗&lt;/mo&gt;\u0000 &lt;mo&gt;̂&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;ℓ&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;≅&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;lim&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mover&gt;\u0000 &lt;mo&gt;⊗&lt;/mo&gt;\u0000 &lt;mo&gt;̂&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ {lim _{krightarrow }} (swidehat{otimes }(ell ^p)_{k}) cong {lim _{krightarrow }}(swidehat{otimes }(c_0)_{-k})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;≤&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$1le ple infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. As a consequence, we obtain that the spaces of slowly and uni","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2740-2748"},"PeriodicalIF":0.8,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On asymptotically almost periodic mild solutions for wave equations on the whole space","authors":"Le The Sac,&nbsp;Pham Truong Xuan","doi":"10.1002/mana.70010","DOIUrl":"https://doi.org/10.1002/mana.70010","url":null,"abstract":"<p>We study the existence, uniqueness and polynomial stability of forward asymptotically almost periodic (AAP-) mild solutions for the wave equation with a singular potential on the whole space <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^n$</annotation>\u0000 </semantics></math> in a framework of weak-<span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^p$</annotation>\u0000 </semantics></math> spaces. First, we use a Yamazaki-type estimate for wave groups on Lorentz spaces to establish the global well-posedness of bounded mild solutions for the corresponding linear wave equations. Then, we provide a Massera-type principle which guarantees the existence of AAP-mild solutions for linear wave equations. Using the results of linear wave equations and fixed point arguments we establish the well-posedness of such solutions for semilinear wave equations. Finally, we obtain a polynomial stability for mild solutions by employing dispersive estimates.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2675-2690"},"PeriodicalIF":0.8,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Six-dimensional complex solvmanifolds with non-invariant trivializing sections of their canonical bundle","authors":"Alejandro Tolcachier","doi":"10.1002/mana.70008","DOIUrl":"https://doi.org/10.1002/mana.70008","url":null,"abstract":"<p>It is known that there exist complex solvmanifolds <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>Γ</mi>\u0000 <mo>∖</mo>\u0000 <mi>G</mi>\u0000 <mo>,</mo>\u0000 <mi>J</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(Gamma backslash G,J)$</annotation>\u0000 </semantics></math> whose canonical bundle is trivialized by a holomorphic section that is not invariant under the action of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math>. The main goal of this paper is to classify the six-dimensional Lie algebras corresponding to such complex solvmanifolds, thus extending the previous work of Fino, Otal, and Ugarte for the invariant case. To achieve this, we complete the classification of six-dimensional solvable strongly unimodular Lie algebras admitting complex structures and identify among them, the ones admitting complex structures with Chern–Ricci flat metrics. Finally, we construct complex solvmanifolds with non-invariant holomorphic sections of their canonical bundle. In particular, we present an example of one such solvmanifold that is not biholomorphic to a complex solvmanifold with an invariant holomorphic section of its canonical bundle. Additionally, we discover a new six-dimensional solvable strongly unimodular Lie algebra equipped with a complex structure that has a nonzero holomorphic (3,0)-form.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2626-2651"},"PeriodicalIF":0.8,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotic stability of the stationary solution to the three-dimensional model of compressible reactive fluid","authors":"Hang Li,&nbsp;Qiwei Wu","doi":"10.1002/mana.70007","DOIUrl":"https://doi.org/10.1002/mana.70007","url":null,"abstract":"<p>In this paper, we consider the asymptotic behavior of solutions to the Cauchy problem for the three-dimensional model of compressible reactive fluid, which can be described by a compressible Navier–Stokes type system with potential external force. First, the existence of the stationary solution is shown in the case that the external force is small enough. Next, making use of the energy method, we prove that the stationary solution is time-asymptotically stable provided that the external force and the initial perturbation are sufficiently small. Finally, we obtain the time-decay rate of the solution toward the stationary solution by combining the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <mo>−</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$L^{p}-L^{q}$</annotation>\u0000 </semantics></math> estimates for the corresponding linear problem and the energy estimates for the nonlinear system.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2596-2625"},"PeriodicalIF":0.8,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions","authors":"Serena Dipierro,&nbsp;Edoardo Proietti Lippi,&nbsp;Caterina Sportelli,&nbsp;Enrico Valdinoci","doi":"10.1002/mana.70006","DOIUrl":"https://doi.org/10.1002/mana.70006","url":null,"abstract":"<p>We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators of mixed order.</p><p>The setting that we introduce is very general and comprises, for instance, the sum of two fractional Laplacians, or of a fractional Laplacian and a Laplacian, as particular cases (the situation in which there are infinitely many operators, and even a continuous distribution of operators, can be considered as well).</p><p>New bits of functional analysis are introduced to deal with this problem. An eigenvalue analysis divides the existence theory into two streams, one related to a mountain pass method, the other to a linking technique.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 8","pages":"2570-2595"},"PeriodicalIF":0.8,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144832614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}