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Unconditional deep-water limit of the intermediate long wave equation in low-regularity. 低正则性中长波方程的无条件深水极限。
IF 1.1 4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2025-01-01 Epub Date: 2025-02-18 DOI: 10.1007/s00030-025-01037-7
Justin Forlano, Guopeng Li, Tengfei Zhao
{"title":"Unconditional deep-water limit of the intermediate long wave equation in low-regularity.","authors":"Justin Forlano, Guopeng Li, Tengfei Zhao","doi":"10.1007/s00030-025-01037-7","DOIUrl":"https://doi.org/10.1007/s00030-025-01037-7","url":null,"abstract":"<p><p>In this paper, we establish the unconditional deep-water limit of the intermediate long wave equation (ILW) to the Benjamin-Ono equation (BO) in low-regularity Sobolev spaces on both the real line and the circle. Our main tool is new unconditional uniqueness results for ILW in <math><msup><mi>H</mi> <mi>s</mi></msup> </math> when <math> <mrow><msub><mi>s</mi> <mn>0</mn></msub> <mo><</mo> <mi>s</mi> <mo>≤</mo> <mfrac><mn>1</mn> <mn>4</mn></mfrac> </mrow> </math> on the line and <math> <mrow><msub><mi>s</mi> <mn>0</mn></msub> <mo><</mo> <mi>s</mi> <mo><</mo> <mfrac><mn>1</mn> <mn>2</mn></mfrac> </mrow> </math> on the circle, where <math> <mrow><msub><mi>s</mi> <mn>0</mn></msub> <mo>=</mo> <mn>3</mn> <mo>-</mo> <msqrt><mrow><mn>33</mn> <mo>/</mo> <mn>4</mn></mrow> </msqrt> <mo>≈</mo> <mn>0.1277</mn></mrow> </math> . Here, we adapt the strategy of Moşincat-Pilod (Pure Appl Anal 5:285-322, 2023) for BO to the setting of ILW by viewing ILW as a perturbation of BO and making use of the smoothing property of the perturbation term.</p>","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"32 2","pages":"28"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11836242/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143469789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonlinear SPDEs and Maximal Regularity: An Extended Survey. 非线性偏微分方程与极大正则性的扩展研究。
IF 1.2 4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2025-01-01 Epub Date: 2025-09-01 DOI: 10.1007/s00030-025-01090-2
Antonio Agresti, Mark Veraar
{"title":"Nonlinear SPDEs and Maximal Regularity: An Extended Survey.","authors":"Antonio Agresti, Mark Veraar","doi":"10.1007/s00030-025-01090-2","DOIUrl":"10.1007/s00030-025-01090-2","url":null,"abstract":"<p><p>In this survey, we provide an in-depth exposition of our recent results on the well-posedness theory for stochastic evolution equations, employing maximal regularity techniques. The core of our approach is an abstract notion of critical spaces, which, when applied to nonlinear SPDEs, coincides with the concept of scaling-invariant spaces. This framework leads to several sharp blow-up criteria and enables one to obtain instantaneous regularization results. Additionally, we refine and unify our previous results, while also presenting several new contributions. In the second part of the survey, we apply the abstract results to several concrete SPDEs. In particular, we give applications to stochastic perturbations of quasi-geostrophic equations, Navier-Stokes equations, and reaction-diffusion systems (including Allen-Cahn, Cahn-Hilliard and Lotka-Volterra models). Moreover, for the Navier-Stokes equations, we establish new Serrin-type blow-up criteria. While some applications are addressed using <math><msup><mi>L</mi> <mn>2</mn></msup> </math> -theory, many require a more general <math> <mrow><msup><mi>L</mi> <mi>p</mi></msup> <mrow><mo>(</mo> <msup><mi>L</mi> <mi>q</mi></msup> <mo>)</mo></mrow> </mrow> </math> -framework. In the final section, we outline several open problems, covering both abstract aspects of stochastic evolution equations, and concrete questions in the study of linear and nonlinear SPDEs.</p>","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"32 6","pages":"123"},"PeriodicalIF":1.2,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12402051/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144993695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On quasi-linear reaction diffusion systems arising from compartmental SEIR models. 关于分区 SEIR 模型产生的准线性反应扩散系统。
IF 1.1 4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2024-01-01 Epub Date: 2024-08-06 DOI: 10.1007/s00030-024-00985-w
Juan Yang, Jeff Morgan, Bao Quoc Tang
{"title":"On quasi-linear reaction diffusion systems arising from compartmental SEIR models.","authors":"Juan Yang, Jeff Morgan, Bao Quoc Tang","doi":"10.1007/s00030-024-00985-w","DOIUrl":"10.1007/s00030-024-00985-w","url":null,"abstract":"<p><p>The global existence and boundedness of solutions to quasi-linear reaction-diffusion systems are investigated. The system arises from compartmental models describing the spread of infectious diseases proposed in Viguerie et al. (Appl Math Lett 111:106617, 2021); Viguerie et al. (Comput Mech 66(5):1131-1152, 2020), where the diffusion rate is assumed to depend on the total population, leading to quasilinear diffusion with possible degeneracy. The mathematical analysis of this model has been addressed recently in Auricchio et al. (Math Methods Appl Sci 46:12529-12548, 2023) where it was essentially assumed that all sub-populations diffuse at the same rate, which yields a positive lower bound of the total population, thus removing the degeneracy. In this work, we remove this assumption completely and show the global existence and boundedness of solutions by exploiting a recently developed <math><msup><mi>L</mi> <mi>p</mi></msup> </math> -energy method. Our approach is applicable to a larger class of systems and is sufficiently robust to allow model variants and different boundary conditions.</p>","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"31 5","pages":"98"},"PeriodicalIF":1.1,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11303479/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141908124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A damped elastodynamics system under the global injectivity condition: local wellposedness in $$L^p$$-spaces 全局注入条件下的阻尼弹性动力学系统:$$L^p$$ -空间中的局部适定性
4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2023-11-04 DOI: 10.1007/s00030-023-00889-1
Sébastien Court
{"title":"A damped elastodynamics system under the global injectivity condition: local wellposedness in $$L^p$$-spaces","authors":"Sébastien Court","doi":"10.1007/s00030-023-00889-1","DOIUrl":"https://doi.org/10.1007/s00030-023-00889-1","url":null,"abstract":"Abstract The purpose of this paper is to model mathematically mechanical aspects of cardiac tissues. The latter constitute an elastic domain whose total volume remains constant. The time deformation of the heart tissue is modeled with the elastodynamics equations dealing with the displacement field as main unknown. These equations are coupled with a pressure whose variations characterize the heart beat. This pressure variable corresponds to a Lagrange multiplier associated with the so-called global injectivity condition. We derive the corresponding coupled system with nonhomogeneous boundary conditions where the pressure variable appears. For mathematical convenience a damping term is added, and for a given class of strain energies we prove the existence of local-in-time solutions in the context of the $$L^p$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> -parabolic maximal regularity.","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"4 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135774232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold 接触子黎曼流形中超曲面的内禀子拉普拉斯
4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2023-10-26 DOI: 10.1007/s00030-023-00891-7
Davide Barilari, Karen Habermann
{"title":"Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold","authors":"Davide Barilari, Karen Habermann","doi":"10.1007/s00030-023-00891-7","DOIUrl":"https://doi.org/10.1007/s00030-023-00891-7","url":null,"abstract":"Abstract We construct and study the intrinsic sub-Laplacian, defined outside the set of characteristic points, for a smooth hypersurface embedded in a contact sub-Riemannian manifold. We prove that, away from characteristic points, the intrinsic sub-Laplacian arises as the limit of Laplace–Beltrami operators built by means of Riemannian approximations to the sub-Riemannian structure using the Reeb vector field. We carefully analyse three families of model cases for this setting obtained by considering canonical hypersurfaces embedded in model spaces for contact sub-Riemannian manifolds. In these model cases, we show that the intrinsic sub-Laplacian is stochastically complete and in particular, that the stochastic process induced by the intrinsic sub-Laplacian almost surely does not hit characteristic points.","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"20 1-2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134907020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Pushed fronts in a Fisher–KPP–Burgers system using geometric desingularization 使用几何去具体化的Fisher-KPP-Burgers系统中的推锋
4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2023-10-20 DOI: 10.1007/s00030-023-00890-8
Matt Holzer, Matthew Kearney, Samuel Molseed, Katie Tuttle, David Wigginton
{"title":"Pushed fronts in a Fisher–KPP–Burgers system using geometric desingularization","authors":"Matt Holzer, Matthew Kearney, Samuel Molseed, Katie Tuttle, David Wigginton","doi":"10.1007/s00030-023-00890-8","DOIUrl":"https://doi.org/10.1007/s00030-023-00890-8","url":null,"abstract":"","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135616056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A family of nonlocal degenerate operators: maximum principles and related properties 一类非局部退化算子:极大原理及相关性质
4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2023-10-19 DOI: 10.1007/s00030-023-00892-6
Delia Schiera
{"title":"A family of nonlocal degenerate operators: maximum principles and related properties","authors":"Delia Schiera","doi":"10.1007/s00030-023-00892-6","DOIUrl":"https://doi.org/10.1007/s00030-023-00892-6","url":null,"abstract":"","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135730517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Relation of the Allen–Cahn equations and the Euler equations and applications of the equipartition Allen-Cahn方程与Euler方程的关系及均分的应用
4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2023-10-06 DOI: 10.1007/s00030-023-00888-2
Dimitrios Gazoulis
{"title":"A Relation of the Allen–Cahn equations and the Euler equations and applications of the equipartition","authors":"Dimitrios Gazoulis","doi":"10.1007/s00030-023-00888-2","DOIUrl":"https://doi.org/10.1007/s00030-023-00888-2","url":null,"abstract":"Abstract We will prove that solutions of the Allen–Cahn equations that satisfy the equipartition of the energy can be transformed into solutions of the Euler equations with constant pressure. As a consequence, we obtain De Giorgi type results, that is, the level sets of entire solutions are hyperplanes. Also, we will determine the structure of solutions of the Allen–Cahn system in two dimensions that satisfy the equipartition. In addition, we apply the Leray projection on the Allen–Cahn system and provide some explicit entire solutions. Finally, we obtain some examples of smooth entire solutions of the Euler equations. For specific type of initial conditions, some of these solutions can be extended to the Navier–Stokes equations. The motivation of this paper is to find a transformation that relates the solutions of the Allen–Cahn equations to solutions of the minimal surface equation of one dimension less. We prove this result for equipartitioned solutions in dimension three.","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135347489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Harmonic embeddings of the Stretched Sierpinski Gasket 拉伸席尔平斯基垫片的谐波嵌入
4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2023-10-04 DOI: 10.1007/s00030-023-00877-5
Ugo Bessi
{"title":"Harmonic embeddings of the Stretched Sierpinski Gasket","authors":"Ugo Bessi","doi":"10.1007/s00030-023-00877-5","DOIUrl":"https://doi.org/10.1007/s00030-023-00877-5","url":null,"abstract":"","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135591708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and non-existence results for a semilinear fractional Neumann problem 一类半线性分数阶Neumann问题的存在性与不存在性结果
4区 数学
Nodea-Nonlinear Differential Equations and Applications Pub Date : 2023-10-03 DOI: 10.1007/s00030-023-00886-4
Eleonora Cinti, Francesca Colasuonno
{"title":"Existence and non-existence results for a semilinear fractional Neumann problem","authors":"Eleonora Cinti, Francesca Colasuonno","doi":"10.1007/s00030-023-00886-4","DOIUrl":"https://doi.org/10.1007/s00030-023-00886-4","url":null,"abstract":"Abstract We establish a priori $$L^infty $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>∞</mml:mi> </mml:msup> </mml:math> -estimates for non-negative solutions of a semilinear nonlocal Neumann problem. As a consequence of these estimates, we get non-existence of non-constant solutions under suitable assumptions on the diffusion coefficient and on the nonlinearity. Moreover, we prove an existence result for radial, radially non-decreasing solutions in the case of a possible supercritical nonlinearity, extending to the case $$0<sle 1/2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>s</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> the analysis started in [7].","PeriodicalId":49747,"journal":{"name":"Nodea-Nonlinear Differential Equations and Applications","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135695578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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