Mathematische Nachrichten最新文献

{"title":"Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction","authors":"Vicente Alvarez,&nbsp;Amin Esfahani","doi":"10.1002/mana.202400068","DOIUrl":"https://doi.org/10.1002/mana.202400068","url":null,"abstract":"<p>In this work, we study the existence of various classes of standing waves for a nonlinear Schrödinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state normalized solutions for this system, which serve as local minimizers of the associated functionals. To address the difficulties raised by the potential term, we employ profile decomposition and concentration-compactness principles. The absence of global energy minimizers in critical and supercritical cases leads us to focus on local energy minimizers. Positive results arise in scenarios of partial confinement, attributed to the spectral properties of the associated linear operators. Furthermore, we demonstrate the existence of a second normalized solution using the Mountain-pass geometry, effectively navigating the difficulties posed by the nonlinear terms. We also explore the asymptotic behavior of local minimizers, revealing connections with unique eigenvectors of the linear operators. Additionally, we identify global and blow-up solutions over time under specific conditions, contributing new insights into the dynamics of the system.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1230-1303"},"PeriodicalIF":0.8,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809544","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":"Two-pointed Prym–Brill–Noether loci and coupled Prym–Petri theorem","authors":"Minyoung Jeon","doi":"10.1002/mana.202300581","DOIUrl":"https://doi.org/10.1002/mana.202300581","url":null,"abstract":"<p>We establish two-pointed Prym–Brill–Noether loci with special vanishing at two points, and determine their K-theory classes when the dimensions are as expected. The classes are derived by the applications of a formula for the K-theory of certain vexillary degeneracy loci in type D. In particular, we show a two-pointed version of the Prym–Petri theorem on the expected dimension in the general case, with a coupled Prym–Petri map. Our approach is inspired by the work on pointed cases by Tarasca, and we generalize unpointed cases by De Concini-Pragacz and Welters.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1201-1219"},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809702","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":"Subelliptic \u0000 \u0000 p\u0000 $p$\u0000 -Laplacian spectral problem for Hörmander vector fields","authors":"Mukhtar Karazym,&nbsp;Durvudkhan Suragan","doi":"10.1002/mana.202300513","DOIUrl":"https://doi.org/10.1002/mana.202300513","url":null,"abstract":"<p>Based on variational methods, we study the spectral problem for the subelliptic <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplacian arising from smooth Hörmander vector fields. We derive the smallest eigenvalue, prove its simplicity and isolatedness, establish the positivity of the first eigenfunction, and show Hölder regularity of eigenfunctions with respect to the control distance. Moreover, we determine the best constant for the <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>-Poincaré–Friedrichs inequality for Hörmander vector fields as a byproduct.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1184-1200"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809868","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":"Mori dream bonds and \u0000 \u0000 \u0000 C\u0000 ∗\u0000 \u0000 ${mathbb {C}}^*$\u0000 -actions","authors":"Lorenzo Barban,&nbsp;Eleonora A. Romano,&nbsp;Luis E. Solá Conde,&nbsp;Stefano Urbinati","doi":"10.1002/mana.202300586","DOIUrl":"https://doi.org/10.1002/mana.202300586","url":null,"abstract":"<p>We construct a correspondence between Mori dream regions arising from small modifications of normal projective varieties and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-actions on polarized pairs which are bordisms. Moreover, we show that the Mori dream regions constructed in this way admit a chamber decomposition on which the models are the geometric quotients of the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-action. In addition, we construct, from a given <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-action on a polarized pair for which there exist at least two admissible geometric quotients, a <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-equivariantly birational <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mo>∗</mo>\u0000 </msup>\u0000 <annotation>${mathbb {C}}^*$</annotation>\u0000 </semantics></math>-variety, whose induced action is a bordism, called the pruning of the variety.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1127-1147"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300586","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809869","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":"Strichartz estimates for the Schrödinger and wave equations with a Laguerre potential on the plane","authors":"Haoran Wang","doi":"10.1002/mana.202400168","DOIUrl":"https://doi.org/10.1002/mana.202400168","url":null,"abstract":"<p>In this paper, we obtain a set of Strichartz inequalities for solutions to the Schrödinger and wave equations with a Laguerre potential on the plane. To obtain the desired inequalities, we intend to prove the dispersive estimates for the involved Schrödinger and wave propagators and then a standard <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <msup>\u0000 <mi>T</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$TT^ast$</annotation>\u0000 </semantics></math> argument will enable us to arrive at these inequalities. The proof of the dispersive estimate for the Schödinger propagator relies on a crucial uniform boundedness of a series involving the Bessel functions of the first kind, while the dispersive estimate for the wave equation follows from a sequence of standard steps, such as the Gaussian boundedness of the heat kernel, Bernstein-type inequalities, and Müller–Seeger's subordination formula. We have to verify these classical results in the present setting, which is possible since the spectral properties of the involved Schrödinger operator can be explicitly calculated.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1304-1327"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809867","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 existence of mild solutions for 3D stochastic Boussinesq system in Besov spaces","authors":"Jinyi Sun,&nbsp;Ning Li,&nbsp;Minghua Yang","doi":"10.1002/mana.202300526","DOIUrl":"https://doi.org/10.1002/mana.202300526","url":null,"abstract":"<p>The paper is concerned with the three-dimensional stochastic Boussinesq system driven by an additive white noise, describing the motion of viscous incompressible fluids with density stratification phenomenon in the rotational framework. By striking new balances between the smoothing effects of the Laplacian dissipation and dispersion effects caused by the Coriolis force and density stratification, we prove existence and uniqueness of global mild solutions to the three-dimensional stochastic Boussinesq system for arbitrarily large initial data and stochastic external forces in Besov spaces, provided that the stratification parameter is large enough. Our results can be regarded as a generalization of [Math. Nachr. 290(2017), 613–631] and [Indiana Univ. Math. J. 66(2017), 2037–2070].</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1105-1126"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809866","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 a conjecture on aCM and Ulrich sheaves on degeneracy loci","authors":"Vladimiro Benedetti,&nbsp;Fabio Tanturri","doi":"10.1002/mana.202400324","DOIUrl":"https://doi.org/10.1002/mana.202400324","url":null,"abstract":"<p>In this paper, we address a conjecture by Kleppe and Miró-Roig stating that suitable twists by line bundles (on the smooth locus) of the exterior powers of the normal sheaf of a standard determinantal locus are arithmetically Cohen–Macaulay, and even Ulrich when the locus is linear determinantal. We do so by providing a very simple locally free resolution of such sheaves obtained through the so-called Weyman's Geometric Method.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 4","pages":"1148-1166"},"PeriodicalIF":0.8,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400324","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809884","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":"Sharp convergence rate on Schrödingertype operators","authors":"Meng Wang,&nbsp;Shuijiang Zhao","doi":"10.1002/mana.202400266","DOIUrl":"https://doi.org/10.1002/mana.202400266","url":null,"abstract":"<p>For Schrödinger-type operators in one dimension, we consider the relationship between the convergence rate and the regularity for initial data. By establishing the associated frequency-localized maximal estimates, we prove sharp results up to the endpoints. The optimal range for the wave operator in all dimensions is also obtained.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1082-1096"},"PeriodicalIF":0.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595513","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":"Infinitesimally equivariant bundles on complex manifolds","authors":"Emile Bouaziz","doi":"10.1002/mana.202400284","DOIUrl":"https://doi.org/10.1002/mana.202400284","url":null,"abstract":"<p>We study holomorphic vector bundles equipped with a compatible action of vector field by <i>Lie derivatives</i>. We will show that the dependence of the Lie derivative on a vector field is <i>almost</i> <span></span><math>\u0000 <semantics>\u0000 <mi>O</mi>\u0000 <annotation>$mathcal {O}$</annotation>\u0000 </semantics></math>-linear. More precisely, after an algebraic reformulation, we show that any continuous <span></span><math>\u0000 <semantics>\u0000 <mi>C</mi>\u0000 <annotation>$mathbf {C}$</annotation>\u0000 </semantics></math>-linear Lie algebra splitting of the symbol map from the Atiyah algebra of a vector bundle on a complex manifold is given by a differential operator, which is further of order at most the rank of the bundle plus one. The proof is quite elementary. When the differential operator we obtain has order 0 we have simply a vector bundle with flat connection, so in a sense, our theorem says that we are always a uniformly bounded order away from this simplest case.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"1076-1081"},"PeriodicalIF":0.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595512","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 nonlinear characterization of stochastic completeness of graphs","authors":"Marcel Schmidt,&nbsp;Ian Zimmermann","doi":"10.1002/mana.202400436","DOIUrl":"https://doi.org/10.1002/mana.202400436","url":null,"abstract":"<p>We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem. It is employed to establish a nonlinear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 3","pages":"925-943"},"PeriodicalIF":0.8,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202400436","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595342","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}