Journal de Mathematiques Pures et Appliquees最新文献

{"title":"On the hydrostatic approximation of Navier-Stokes-Maxwell system with Gevrey data","authors":"Ning Liu ,&nbsp;Marius Paicu ,&nbsp;Ping Zhang","doi":"10.1016/j.matpur.2024.05.005","DOIUrl":"10.1016/j.matpur.2024.05.005","url":null,"abstract":"<div><p>In this paper, we prove the local well-posedness of a scaled anisotropic Navier-Stokes-Maxwell system in a 2-D striped domain with initial data around some nonzero background magnetic field in Gevrey-2 class. Then we rigorously justify the limit from the scaled anisotropic equations to the associated hydrostatic system and provide with the precise convergence rate. Finally, with small initial data in Gevrey-<span><math><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> class, we also extend the lifespan of thus obtained solutions to a longer time interval.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the transverse stability of smooth solitary waves in a two-dimensional Camassa–Holm equation","authors":"Anna Geyer ,&nbsp;Yue Liu ,&nbsp;Dmitry E. Pelinovsky","doi":"10.1016/j.matpur.2024.05.008","DOIUrl":"https://doi.org/10.1016/j.matpur.2024.05.008","url":null,"abstract":"<div><p>We consider the propagation of smooth solitary waves in a two-dimensional generalization of the Camassa–Holm equation. We show that transverse perturbations to one-dimensional solitary waves behave similarly to the KP-II theory. This conclusion follows from our two main results: (i) the double eigenvalue of the linearized equations related to the translational symmetry breaks under a transverse perturbation into a pair of the asymptotically stable resonances and (ii) small-amplitude solitary waves are linearly stable with respect to transverse perturbations.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141286064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetry breaking and instability for semilinear elliptic equations in spherical sectors and cones","authors":"Giulio Ciraolo ,&nbsp;Filomena Pacella ,&nbsp;Camilla Chiara Polvara","doi":"10.1016/j.matpur.2024.05.004","DOIUrl":"https://doi.org/10.1016/j.matpur.2024.05.004","url":null,"abstract":"<div><p>We consider semilinear elliptic equations with mixed boundary conditions in spherical sectors inside a cone. The aim of the paper is to show that a radial symmetry result of Gidas-Ni-Nirenberg type for positive solutions does not hold in general nonconvex cones. This symmetry breaking result is achieved by studying the Morse index of radial positive solutions and analyzing how it depends on the domain D on the unit sphere which spans the cone. In particular it is proved that the Neumann eigenvalues of the Laplace Beltrami operator on D play a role in computing the Morse index. A similar breaking of symmetry result is obtained for the positive solutions of the critical Neumann problem in the whole unbounded cone. In this case it is proved that the standard bubbles, which are the only radial solutions, become unstable for a class of nonconvex cones.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000515/pdfft?md5=f8d91cb0d64ebc67a3dd4f2bea70bb4e&pid=1-s2.0-S0021782424000515-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141263820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The five gradients inequality on differentiable manifolds","authors":"Simone Di Marino ,&nbsp;Simone Murro ,&nbsp;Emanuela Radici","doi":"10.1016/j.matpur.2024.05.007","DOIUrl":"10.1016/j.matpur.2024.05.007","url":null,"abstract":"<div><p>The goal of this paper is to derive the so-called five gradients inequality for optimal transport theory for general cost functions on two class of differentiable manifolds: locally compact Lie groups and compact Riemannian manifolds.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000540/pdfft?md5=317b8328f86476b25594b613d838545a&pid=1-s2.0-S0021782424000540-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subwavelength resonant acoustic scattering in fast time-modulated media","authors":"F. Feppon ,&nbsp;H. Ammari","doi":"10.1016/j.matpur.2024.05.012","DOIUrl":"10.1016/j.matpur.2024.05.012","url":null,"abstract":"<div><p>This article provides a rigorous mathematical analysis of acoustic wave scattering induced by a high-contrast subwavelength resonator whose material density is periodically modulated in time, and with a modulation frequency that is much larger than the one of the incident wave. We find that in general, the effect of the fast modulation is averaged over time and that the system behaves as an unmodulated resonator with an apparent effective density. However, under a suitable tuning of the modulation, which achieves a matching between temporal Sturm-Liouville and spatial Neumann eigenvalues, the low frequency incident wave becomes suddenly able to excite high frequency modes in the resonator. This phenomenon leads to the generation of scattered waves carrying high frequency components in the far field, and to the existence of exponentially growing outgoing modes. From these findings, it is expected that such time-modulated system could serve as a spontaneously radiating device, or as a high harmonic generator.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Well-posedness theory for non-homogeneous incompressible fluids with odd viscosity","authors":"Francesco Fanelli ,&nbsp;Rafael Granero-Belinchón ,&nbsp;Stefano Scrobogna","doi":"10.1016/j.matpur.2024.05.006","DOIUrl":"https://doi.org/10.1016/j.matpur.2024.05.006","url":null,"abstract":"<div><p>Several fluid systems are characterised by time reversal and parity breaking. Examples of such phenomena arise both in quantum and classical hydrodynamics. In these situations, the viscosity tensor, often dubbed “odd viscosity”, becomes non-dissipative. At the mathematical level, this fact translates into a loss of derivatives at the level of <em>a priori</em> estimates: while the odd viscosity term depends on derivatives of the velocity field, no parabolic smoothing effect can be expected.</p><p>In the present paper, we establish a well-posedness theory in Sobolev spaces for a system of incompressible non-homogeneous fluids with odd viscosity. The crucial point of the analysis is the introduction of a set of <em>good unknowns</em>, which allow for the emerging of a hidden hyperbolic structure underlying the system of equations. It is exactly this hyperbolic structure which makes it possible to circumvent the derivative loss and propagate high enough Sobolev norms of the solution. The well-posedness result is local in time; two continuation criteria are also established.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141250357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal stability results and nonlinear duality for L∞ entropy and L1 viscosity solutions","authors":"Nathaël Alibaud ,&nbsp;Jørgen Endal ,&nbsp;Espen R. Jakobsen","doi":"10.1016/j.matpur.2024.05.003","DOIUrl":"10.1016/j.matpur.2024.05.003","url":null,"abstract":"<div><p>We give a new and rigorous duality relation between two central notions of weak solutions of nonlinear PDEs: entropy and viscosity solutions. It takes the form of the <em>nonlinear dual inequality:</em><span><span><span>(⋆)</span><span><math><mo>∫</mo><mo>|</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><msub><mrow><mi>S</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>|</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>0</mn></mrow></msub><mspace></mspace><mi>d</mi><mi>x</mi><mo>≤</mo><mo>∫</mo><mo>|</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>−</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>|</mo><msub><mrow><mi>G</mi></mrow><mrow><mi>t</mi></mrow></msub><msub><mrow><mi>φ</mi></mrow><mrow><mn>0</mn></mrow></msub><mspace></mspace><mi>d</mi><mi>x</mi><mo>,</mo><mspace></mspace><mo>∀</mo><msub><mrow><mi>φ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>≥</mo><mn>0</mn><mo>,</mo><mo>∀</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mo>∀</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo></math></span></span></span> where <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> is the entropy solution semigroup of the anisotropic degenerate parabolic equation<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>u</mi><mo>+</mo><mrow><mi>div</mi></mrow><mi>F</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>=</mo><mrow><mi>div</mi></mrow><mo>(</mo><mi>A</mi><mo>(</mo><mi>u</mi><mo>)</mo><mi>D</mi><mi>u</mi><mo>)</mo><mo>,</mo></math></span></span></span> and where we look for the smallest semigroup <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> satisfying <span>(⋆)</span>. This amounts to finding an optimal weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> contraction estimate for <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span>. Our main result is that <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> is the viscosity solution semigroup of the Hamilton-Jacobi-Bellman equation<span><span><span><math><msub><mrow><mo>∂</mo></mrow><mrow><mi>t</mi></mrow></msub><mi>φ</mi><mo>=</mo><msub><mrow><mi>sup</mi></mrow><mrow><mi>ξ</mi></mrow></msub><mo>⁡</mo><mo>{</mo><msup><mrow><mi>F</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>ξ</mi><mo>)</mo><mo>⋅</mo><mi>D</mi><mi>φ</mi><mo>+</mo><mtext>tr</mtext><mo>(</mo><mi>A</mi><mo>(</mo><mi>ξ</mi><mo>)</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>φ</mi><mo>)</mo><mo>}</mo><mo>.</mo></math></span></span></span> Since weighted <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> contraction results are mainly used for possibly n","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000503/pdfft?md5=dab8d6332cc3822ca14f90b02cc59d6f&pid=1-s2.0-S0021782424000503-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lp maximal regularity for vector-valued Schrödinger operators","authors":"Davide Addona ,&nbsp;Vincenzo Leone ,&nbsp;Luca Lorenzi ,&nbsp;Abdelaziz Rhandi","doi":"10.1016/j.matpur.2024.05.010","DOIUrl":"https://doi.org/10.1016/j.matpur.2024.05.010","url":null,"abstract":"<div><p>In this paper we consider the vector-valued Schrödinger operator <span><math><mo>−</mo><mi>Δ</mi><mo>+</mo><mi>V</mi></math></span>, where the potential term <em>V</em> is a matrix-valued function whose entries belong to <span><math><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span> and, for every <span><math><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mi>V</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> is a symmetric and nonnegative definite matrix, with non positive off-diagonal terms and with eigenvalues comparable each other. For this class of potential terms we obtain maximal inequality in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></math></span>. Assuming further that the minimal eigenvalue of <em>V</em> belongs to some reverse Hölder class of order <span><math><mi>q</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>∪</mo><mo>{</mo><mo>∞</mo><mo>}</mo></math></span>, we obtain maximal inequality in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></math></span>, for <em>p</em> in between 1 and some <em>q</em>, and generation results.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141263821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of bulk-surface reaction-sorption-diffusion systems with Langmuir-type adsorption","authors":"Björn Augner,&nbsp;Dieter Bothe","doi":"10.1016/j.matpur.2024.05.001","DOIUrl":"10.1016/j.matpur.2024.05.001","url":null,"abstract":"<div><p>We consider a class of bulk-surface reaction-adsorption-diffusion systems, i.e. a coupled system of reaction-diffusion systems on a bounded domain <span><math><mi>Ω</mi><mo>⊆</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> (bulk phase) and its boundary <span><math><mi>Σ</mi><mo>=</mo><mo>∂</mo><mi>Ω</mi></math></span> (surface phase), which are coupled via nonlinear normal flux boundary conditions. In particular, this class includes a heterogeneous catalysis model with Fickian bulk and surface diffusion and nonlinear adsorption of Langmuir type, i.e. transport from the bulk phase to the active surface, and desorption. For this model, we obtain well-posedness, positivity and global-in-time existence of solutions under some realistic structural conditions on the chemical reaction network and the sorption model. We work in appropriate Sobolev-Slobodetskii settings, where we aim for a wide range for the integrability index, including in particular values <span><math><mi>p</mi><mo>&lt;</mo><mi>d</mi></math></span>.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000485/pdfft?md5=4cc380ed54d79a86848e81405b723443&pid=1-s2.0-S0021782424000485-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability for the Helmholtz equation in deterministic and random periodic structures","authors":"Gang Bao ,&nbsp;Yiwen Lin ,&nbsp;Xiang Xu","doi":"10.1016/j.matpur.2024.05.014","DOIUrl":"10.1016/j.matpur.2024.05.014","url":null,"abstract":"<div><p>Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the stability estimate for the Helmholtz equation in a deterministic periodic structure is established. For the stochastic case, by introducing a variable transform, the variational formulation of the scattering problem in a random domain is reduced to that in a definite domain with random medium. Combining the stability result for the deterministic case with regularity and stochastic regularity of the scattering surface, Pettis measurability theorem and Bochner's Theorem further yield the stability result for the scattering problem by random periodic structures. Both stability estimates are explicit with respect to the wavenumber.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}