Mathematische Nachrichten最新文献

{"title":"Two Monotone Quantities Along the Inverse Mean Curvature Flow in \u0000 \u0000 \u0000 H\u0000 n\u0000 \u0000 $mathbb {H}^{n}$","authors":"Jia Li","doi":"10.1002/mana.70160","DOIUrl":"https://doi.org/10.1002/mana.70160","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we derive two monotone quantities along the inverse mean curvature flow (IMCF) in hyperbolic space <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {H}^{n}$</annotation>\u0000 </semantics></math>. First, we prove that the quantity <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>(</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$G(t)$</annotation>\u0000 </semantics></math> is increasing along the IMCF, which relates the weighted volume enclosed by hypersurface and the weighted total mean curvature of the hypersurface. Second, we prove that the first eigenvalue of <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplacian of the free boundary hypersurfaces supported on the geodesic spheres of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {H}^{n}$</annotation>\u0000 </semantics></math> is decreasing along the IMCF.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1588-1595"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395030","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":"Global Well-Posedness and Exponential Decay of Two-Dimensional Nonhomogeneous Micropolar System With Density-Dependent Viscosities","authors":"Cheng Cheng,&nbsp;Mingyu Zhang","doi":"10.1002/mana.70165","DOIUrl":"https://doi.org/10.1002/mana.70165","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper concerns the two-dimensional nonhomogeneous micropolar system with density-dependent viscosities and vacuum. Based on the energy method and the structural characteristics of the model, we establish the global well-posdeness and exponential decay of strong solutions provided that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>∥</mo>\u0000 <mo>∇</mo>\u0000 <mi>μ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>ρ</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mo>∥</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 </msub>\u0000 <mrow>\u0000 <mo>+</mo>\u0000 <mo>∥</mo>\u0000 <mo>∇</mo>\u0000 <mi>ξ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>ρ</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <msub>\u0000 <mo>∥</mo>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 </msub>\u0000 <mo>+</mo>\u0000 <msub>\u0000 <mrow>\u0000 <mo>∥</mo>\u0000 <mo>∇</mo>\u0000 <mi>λ</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>ρ</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mo>∥</mo>\u0000 </mrow>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 </msub>\u0000 <mo>⩽</mo>\u0000 <mi>ε</mi>\u0000 </mrow>\u0000 <annotation>$Vert nabla mu (rho _0)Vert _{L^q}+Vert nabla xi (rho _0)Vert _{L^q}+Vert nabla lambda (rho _0)Vert _{L^q}leqslant varepsilon$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mi>∞</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$qin (2, infty)$</annotation>\u0000 </semantics></math>.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1692-1715"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395062","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":"Four-Dimensional pp-Wave Lie Groups and Harmonic Curvature","authors":"E. García-Río,&nbsp;R. Rodríguez-Gigirey,&nbsp;R. Vázquez-Lorenzo","doi":"10.1002/mana.70168","DOIUrl":"https://doi.org/10.1002/mana.70168","url":null,"abstract":"<p>We determine all four-dimensional Lie groups which have harmonic curvature. In parallel, a description of four-dimensional pp-wave Lie groups is obtained.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1751-1780"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70168","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395151","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":"A Note on Sobolev-Lorentz Capacity and Hausdorff Measure","authors":"Daniel Campbell","doi":"10.1002/mana.70157","DOIUrl":"https://doi.org/10.1002/mana.70157","url":null,"abstract":"<p>In this paper, we give an elementary proof that sets of zero <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$p,1$</annotation>\u0000 </semantics></math>-Sobolev-Lorentz capacity are <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathcal {H}^{n-p}$</annotation>\u0000 </semantics></math>-null sets, independently of nonlinear potential theory. We further show that there exists a set of Sobolev-Lorentz-<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(p,1)$</annotation>\u0000 </semantics></math> capacity equal to zero with Hausdorff dimension equal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 <annotation>$n-p$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1540-1548"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70157","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395067","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":"Closed Geodesics and Isometries on Compact Lorentz Solvmanifolds","authors":"Pablo R. Montenegro,&nbsp;Gabriela P. Ovando","doi":"10.1002/mana.70166","DOIUrl":"https://doi.org/10.1002/mana.70166","url":null,"abstract":"<div>\u0000 \u0000 <p>The aim of this work is a deep study of existence of closed geodesics on Lorentz homogeneous spaces of the form <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>M</mi>\u0000 <mo>=</mo>\u0000 <mi>G</mi>\u0000 <mo>/</mo>\u0000 <mi>Λ</mi>\u0000 </mrow>\u0000 <annotation>$M=G/Lambda$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is a solvable Lie group endowed with a bi-invariant Lorentz metric and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Λ</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation>$Lambda &lt; G$</annotation>\u0000 </semantics></math> is a cocompact lattice. Conditions to assert closedness of light, time, or spacelike geodesics on the compact quotient spaces are given. This study implicitly requires additional information about the lattices in each case. We found conditions for which every lightlike geodesic on the quotient space is closed. And more importantly, this situation depends on the lattice. Even in dimension 4, there are examples of compact solvmanifolds for which every lightlike geodesic is closed and others for which at every point there is only one direction in which lightlike geodesics close. For time and spacelike geodesics, the conclusions are different: There are both open and closed geodesics of type timelike and spacelike. Finally, we improve results of isometry groups on compact quotients, for which one needs information on the normalizer of the given lattice. We show that this normalizer is included in a certain subset, if some extra condition holds. Moreover this condition is related to that one that determines if every lightlike geodesic on <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> is closed. We show explicit computations in dimensions four and six.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1716-1736"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395116","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":"Periodic Solutions of Third-Order Mixed Degenerate Differential Equations With Two Infinite Delays in Vector-Valued Function Spaces","authors":"Shangquan Bu,&nbsp;Gang Cai","doi":"10.1002/mana.70154","DOIUrl":"https://doi.org/10.1002/mana.70154","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;The aim of this paper is to consider the well-posedness of third-order mixed degenerate differential equation with two infinite delays &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;msub&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(P_3)$&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;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/msup&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;mo&gt;′&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&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;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/msup&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;mi&gt;A&lt;/mi&gt;\u0000 &lt;mi&gt;u&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;mi&gt;B&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;′&lt;/mo&gt;\u0000 &lt;/msup&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;msubsup&gt;\u0000 &lt;mo&gt;∫&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mi&gt;d&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;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1526-1539"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148394951","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":"Dimension-Independent Functional Inequalities by Tensorization and Projection Arguments","authors":"Fabrice Baudoin,&nbsp;Maria Gordina,&nbsp;Rohan Sarkar","doi":"10.1002/mana.70164","DOIUrl":"https://doi.org/10.1002/mana.70164","url":null,"abstract":"<div>\u0000 \u0000 <p>We study stability under tensorization and projection-type operations of gradient estimates and other functional inequalities for Markov semigroups on metric spaces. Using transportation inequalities obtained by Baudoin and Eldredge in 2021, we prove that constants in the gradient estimates can be chosen to be dimension-independent. Our results are applicable to hypoelliptic diffusions on sub-Riemannian manifolds and some hypocoercive diffusions. As a byproduct, we obtain dimension-independent reverse Poincaré inequality, reverse logarithmic Sobolev inequality, and gradient bounds on Lie groups with transverse symmetries and for non-isotropic Heisenberg groups.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1665-1691"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395182","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":"Trace Formulas in Higher Dimensions","authors":"Arup Chattopadhyay,&nbsp;Saikat Giri,&nbsp;Chandan Pradhan,&nbsp;Alexandr Usachev","doi":"10.1002/mana.70170","DOIUrl":"https://doi.org/10.1002/mana.70170","url":null,"abstract":"<div>\u0000 \u0000 <p>The paper establishes the Krein and Koplienko trace formulas for multivariable operator functions on symmetrically normed ideals of bounded operators. Results are proved for self-adjoint and maximal dissipative operators. They cover both ideals with normal and singular traces. The admissible function classes considered in the trace formulas include both analytic and nonanalytic scalar functions. Results are illustrated with examples.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1795-1832"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395210","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":"Arakelov Geometry of Cuntz–Pimsner Algebras","authors":"Igor V. Nikolaev","doi":"10.1002/mana.70158","DOIUrl":"https://doi.org/10.1002/mana.70158","url":null,"abstract":"<div>\u0000 \u0000 <p>We use <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-theory of the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>$C^*$</annotation>\u0000 </semantics></math>-algebras to study the Arakelov geometry, i.e., a compactification of the arithmetic schemes <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mo>→</mo>\u0000 <mo>Spec</mo>\u0000 <mspace></mspace>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 <annotation>$Vrightarrow operatorname{Spec} nobreakspace mathbf {Z}$</annotation>\u0000 </semantics></math>. In particular, it is proved that the Picard group of <span></span><math>\u0000 <semantics>\u0000 <mi>V</mi>\u0000 <annotation>$V$</annotation>\u0000 </semantics></math> is isomorphic to the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$K_0$</annotation>\u0000 </semantics></math>-group of a Cuntz–Pimsner algebra associated with <span></span><math>\u0000 <semantics>\u0000 <mi>V</mi>\u0000 <annotation>$V$</annotation>\u0000 </semantics></math>. We apply this result to the finiteness problem for the algebraic varieties over number fields.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1549-1555"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395049","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":"Unique Continuation Property for the Coupled Ostrovsky System","authors":"Ricardo Córdoba,&nbsp;Alex M. Montes","doi":"10.1002/mana.70147","DOIUrl":"https://doi.org/10.1002/mana.70147","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we establish a result of unique continuation for the coupled Ostrovsky system that models the evolution of long water waves with small amplitude in the presence of surface tension. More precisely, we will show that if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>,</mo>\u0000 <mi>t</mi>\u0000 <mo>)</mo>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(u,v) =(u(x, t), v(x, t))$</annotation>\u0000 </semantics></math> is a solution of the nonlinear system, in a suitable function space, and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(u,v)$</annotation>\u0000 </semantics></math> vanishes on an open subset <span></span><math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 <mo>×</mo>\u0000 <mo>[</mo>\u0000 <mo>−</mo>\u0000 <mi>T</mi>\u0000 <mo>,</mo>\u0000 <mi>T</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {R}times [-T, T]$</annotation>\u0000 </semantics></math>, then <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>u</mi>\u0000 <mo>,</mo>\u0000 <mi>v</mi>\u0000 <mo>)</mo>\u0000 <mo>≡</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$(u,v)equiv 0$</annotation>\u0000 </semantics></math> in the horizontal component of <span></span><math>\u0000 <semantics>\u0000 <mi>Ω</mi>\u0000 <annotation>$Omega$</annotation>\u0000 </semantics></math>. To state such property, we use a Carleman-type estimate for a differential operator <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$mathcal {L}$</annotation>\u0000 </semantics></math> related to the system. We prove the Carleman estimate using a particular version of the well-known Treves' inequality.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 6","pages":"1358-1372"},"PeriodicalIF":0.8,"publicationDate":"2026-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148160786","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}