Mathematische Nachrichten最新文献

{"title":"Singular integral operators and commutators on two-weight Morrey spaces","authors":"Meichuan Lv,&nbsp;Wenming Li","doi":"10.1002/mana.12007","DOIUrl":"https://doi.org/10.1002/mana.12007","url":null,"abstract":"<p>In this paper, we obtain the mapping properties for the Hardy–Littlewood maximal operator, Calderón–Zygmund singular integral operators, and the commutators of the singular integral operators with the <span></span><math>\u0000 <semantics>\u0000 <mtext>BMO</mtext>\u0000 <annotation>$text{BMO}$</annotation>\u0000 </semantics></math> functions on the two-weight Morrey spaces. We also get the endpoint estimates for the commutators on the two-weight Morrey spaces.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1713-1726"},"PeriodicalIF":0.8,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930329","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":"Angular distribution toward the points of the neighbor-flips modular curve seen by a fast moving observer","authors":"Jack Anderson,&nbsp;Florin P. Boca,&nbsp;Cristian Cobeli,&nbsp;Alexandru Zaharescu","doi":"10.1002/mana.12016","DOIUrl":"https://doi.org/10.1002/mana.12016","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;annotation&gt;$h$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be a fixed non-zero integer. For every &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$tin mathbb {R}_+$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and every prime &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;, consider the angles between rays from an observer located at the point &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(-tJ_p^2,0)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on the real axis toward the set of all integral solutions &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(x,y)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of the equation &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;y&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;≡&lt;/mo&gt;\u0000 &lt;mi&gt;h&lt;/mi&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mi&gt;mod&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$y^{-1}-x^{-1}equiv h left(mathrm{ mod;}pright)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in the square &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&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;msub&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1617-1632"},"PeriodicalIF":0.8,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930387","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":"Anisotropic quasilinear elliptic systems with homogeneous critical nonlinearities","authors":"Mathew Gluck","doi":"10.1002/mana.12008","DOIUrl":"https://doi.org/10.1002/mana.12008","url":null,"abstract":"<p>In this work, we consider a system of quasilinear elliptic equations driven by an anisotropic <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplacian. The lower order nonlinearities are in potential form and exhibit critical Sobolev growth. We exhibit conditions on the coefficients of the differential operator, the domain of the unknown function, and the lower order nonlinearities under which nontrivial solutions are guaranteed to exist and conditions on these objects under which a nontrivial solution does not exist.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1633-1662"},"PeriodicalIF":0.8,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930330","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":"Nonlocal problem with critical exponential nonlinearity of the convolution type: A non-resonant case","authors":"Suman Kanungo,&nbsp;Pawan Kumar Mishra","doi":"10.1002/mana.202400383","DOIUrl":"https://doi.org/10.1002/mana.202400383","url":null,"abstract":"<p>In this paper, we study the following class of weighted Choquard equations:\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1578-1616"},"PeriodicalIF":0.8,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930392","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 computation of Kähler differentials and characterizations of Galois extensions with independent defect","authors":"Steven Dale Cutkosky,&nbsp;Franz-Viktor Kuhlmann,&nbsp;Anna Rzepka","doi":"10.1002/mana.202300532","DOIUrl":"https://doi.org/10.1002/mana.202300532","url":null,"abstract":"<p>For important cases of algebraic extensions of valued fields, we develop presentations of the associated Kähler differentials of the extensions of their valuation rings. We compute their annihilators as well as the associated differents. We then apply the results to Galois defect extensions of prime degree. Defects can appear in finite extensions of valued fields of positive residue characteristic and are serious obstructions to several problems in positive characteristic. A classification of defects (dependent vs. independent) has been introduced by the second and the third author. It has been shown that perfectoid fields and deeply ramified fields only admit extensions with independent defect. We give several characterizations of independent defect, using ramification ideals, Kähler differentials, and traces of the maximal ideals of valuation rings. All of our results are for arbitrary valuations; in particular, we have no restrictions on their ranks or value groups.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1549-1577"},"PeriodicalIF":0.8,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930402","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":"Characterization of Besov spaces with dominating mixed smoothness by differences","authors":"Paul Nikolaev,&nbsp;David J. Prömel,&nbsp;Mathias Trabs","doi":"10.1002/mana.202400122","DOIUrl":"https://doi.org/10.1002/mana.202400122","url":null,"abstract":"<p>Besov spaces with dominating mixed smoothness, on the product of the real line and the torus as well as bounded domains, are studied. A characterization of these function spaces in terms of differences is provided. Applications to random fields, like Gaussian fields and the stochastic heat equation, are discussed, based on a Kolmogorov criterion for Besov regularity with dominating mixed smoothness.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2116-2151"},"PeriodicalIF":0.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657588","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":"Local \u0000 \u0000 H\u0000 $H$\u0000 -principles for holomorphic partial differential relations","authors":"Luis Giraldo,&nbsp;Guillermo Sánchez-Arellano","doi":"10.1002/mana.202300492","DOIUrl":"https://doi.org/10.1002/mana.202300492","url":null,"abstract":"<p>We introduce the notion of the realifications of an arbitrary <i>holomorphic partial differential relation</i> <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$mathcal {R}$</annotation>\u0000 </semantics></math>, that are partial differential relations associated with the restrictions of <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$mathcal {R}$</annotation>\u0000 </semantics></math> to totally real submanifolds of maximal dimension. Our main result states that if any realification of an open holomorphic partial differential relation over a Stein manifold satisfies a relative to domain <span></span><math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-principle, then it is possible to deform any formal solution into one that is holonomic in a neighborhood of a Lagrangian skeleton of the Stein manifold. If the Stein manifold is an open Riemann surface or it has finite type, then that skeleton is independent of the formal solution. This yields the existence of local <span></span><math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-principles over that skeleton. These results broaden those obtained by Forstnerič and Slapar on holomorphic immersions, submersions, and complex contact structures for instance to holomorphic local <span></span><math>\u0000 <semantics>\u0000 <mi>h</mi>\u0000 <annotation>$h$</annotation>\u0000 </semantics></math>-principles for the corresponding version in the complex category of some other classical examples of distributions and structures in the smooth category such as complex even contact, complex Engel, and complex twisted locally conformal symplectic structures.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1521-1548"},"PeriodicalIF":0.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930303","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":"Regularity criteria for the three-dimensional axisymmetric Boussinesq equations in anisotropic Lorentz spaces","authors":"Zhouyu Li","doi":"10.1002/mana.202400237","DOIUrl":"https://doi.org/10.1002/mana.202400237","url":null,"abstract":"<p>We establish regularity criteria of the three-dimensional axisymmetric Boussinesq equations in anisotropic Lorentz spaces. In particular, no a priori assumptions on the temperature are imposed, and our result improves and extends the related result of Chae and Lee.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 7","pages":"2105-2115"},"PeriodicalIF":0.8,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144657591","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":"Reducibility of ultra-differentiable quasi-periodic linear systems","authors":"Xiangyuan Zhang,&nbsp;Dongfeng Zhang","doi":"10.1002/mana.202300122","DOIUrl":"https://doi.org/10.1002/mana.202300122","url":null,"abstract":"&lt;p&gt;In ultra-differentiable classes, this paper studies the reducibility of the quasi-periodic linear system &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;̇&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&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;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$dot{x}=(A+varepsilon Q(t))x,xin mathbb {R}^{d}$&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;A&lt;/mi&gt;\u0000 &lt;annotation&gt;$A$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a constant matrix with different eigenvalues &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mtext&gt;…&lt;/mtext&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$lambda =(lambda _{1},lambda _{2},ldots,lambda _{d})$&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;mi&gt;Q&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Q(t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a ultra-differentiable quasi-periodic matrix with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;annotation&gt;$r$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; basic frequencies &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1482-1495"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930472","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 Cauchy problem of three-dimensional compressible magneto-micropolar fluids with vacuum","authors":"Mingyu Zhang","doi":"10.1002/mana.202400144","DOIUrl":"https://doi.org/10.1002/mana.202400144","url":null,"abstract":"<p>In this paper, we study the Cauchy problem of three-dimensional compressible magneto-micropolar fluids. Applying the energy method and the structural characteristics of the model, the global existence and uniqueness of classical solutions are established provided that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>∥</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <msub>\u0000 <mo>∥</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$Vert mathbf { B}_0Vert _{L^3}+M_0$</annotation>\u0000 </semantics></math> is suitable small, where <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$mathbf { B}_0$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$M_0$</annotation>\u0000 </semantics></math> represent the initial magnetic field and upper bound of initial density. It is worth mentioning that both the vacuum states of initial density and the possible random largeness of initial energy are allowed. Thus, the results obtained particularly extend the one due to Wei et al., where the global well-posedness of smooth solutions with small perturbations of initial data was proved.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 5","pages":"1449-1481"},"PeriodicalIF":0.8,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930471","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}