Journal of Mathematical Fluid Mechanics最新文献_第3页

Global Weak Solutions in a Three-dimensional Keller–Segel–Navier–Stokes System with Flux Limitation and Superlinear Production 具有通量限制和超线性产生的三维Keller-Segel-Navier-Stokes系统的全局弱解

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-07-11 DOI: 10.1007/s00021-025-00958-8

Jiyuan Guo, Shohei Kohatsu, Tomomi Yokota

{"title":"Global Weak Solutions in a Three-dimensional Keller–Segel–Navier–Stokes System with Flux Limitation and Superlinear Production","authors":"Jiyuan Guo, Shohei Kohatsu, Tomomi Yokota","doi":"10.1007/s00021-025-00958-8","DOIUrl":"10.1007/s00021-025-00958-8","url":null,"abstract":"<div><p>This paper is concerned with a three-dimensional Keller–Segel–Navier–Stokes system incorporating singular flux limitation and superlinear production. The primary goal is to establish global existence of weak solutions under conditions ensuring that flux limitations suppress the blow-up tendencies induced by superlinear growth. More precisely, this paper focuses on the system </p><div><figure><div><div><picture><img></picture></div></div></figure></div><p> in a bounded domain <span>(Omega subset mathbb {R}^3)</span> with smooth boundary, where <span>(0< alpha < 1)</span> and <span>(beta ge 1)</span>. Under the assumption <span>(alpha > 1 - frac{1}{3beta -1})</span>, we prove global existence of weak solutions to the Neumann problem for <span>((*))</span>. This study extends the previous work by Winkler [27], in which the corresponding system with the regular sensitivity <span>((|nabla c|^2+1)^{-frac{alpha }{2}})</span> and the linear production <span>((beta =1))</span> was considered, and highlights how strong flux limitation can control the effects of superlinear growth.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164481","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}

引用次数: 0

Global Strong Solutions to the Cauchy Problem of Three-dimensional Isentropic Magnetohydrodynamics Equations with Large Initial Data 具有大初始数据的三维等熵磁流体动力学方程Cauchy问题的全局强解

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-07-07 DOI: 10.1007/s00021-025-00960-0

Yachun Li, Peng Lu, Zhaoyang Shang

引用次数: 0

Inhomogenous Navier–Stokes Equations with Unbounded Density 密度无界的非齐次Navier-Stokes方程

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-07-07 DOI: 10.1007/s00021-025-00956-w

Jean-Paul Adogbo, Piotr B. Mucha, Maja Szlenk

{"title":"Inhomogenous Navier–Stokes Equations with Unbounded Density","authors":"Jean-Paul Adogbo, Piotr B. Mucha, Maja Szlenk","doi":"10.1007/s00021-025-00956-w","DOIUrl":"10.1007/s00021-025-00956-w","url":null,"abstract":"<div><p>In the current state of the art regarding the Navier–Stokes equations, the existence of unique solutions for incompressible flows in two spatial dimensions is already well-established. Recently, these results have been extended to models with variable density, maintaining positive outcomes for merely bounded densities, even in cases with large vacuum regions. However, the study of incompressible Navier-Stokes equations with unbounded densities remains incomplete. Addressing this gap is the focus of the present paper. Our main result demonstrates the global existence of a unique solution for flows initiated by unbounded density, whose regularity/integrability is characterized within a specific subset of the Yudovich class of unbounded functions. The core of our proof lies in the application of Desjardins’ inequality, combined with a blow-up criterion for ordinary differential equations. Furthermore, we derive time-weighted estimates that guarantee the existence of a <span>(C^1)</span> velocity field and ensure the equivalence of Eulerian and Lagrangian formulations of the equations. Finally, by leveraging results from Danchin, R., Mucha, P.B.: The incompressible Navier-Stokes equations in vacuum. Comm. Pure Appl. Math <b>72</b>(7), 1351–1385 (2019), we conclude the uniqueness of the solution.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00956-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163074","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}

引用次数: 0

Blowup Phenomenon of Ideal Compressible Non-isentropic Magnetohydrodynamic Equations with Radius Weighted Functional 半径加权泛函理想可压缩非等熵磁流体动力学方程的爆破现象

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-07-02 DOI: 10.1007/s00021-025-00957-9

Kar Hung Wong, Sen Wong, Manwai Yuen

引用次数: 0

Regularity, Uniqueness and the Relative Size of Small and Large Scales in SQG Flows SQG流的规律性、唯一性及小尺度和大尺度的相对大小

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-30 DOI: 10.1007/s00021-025-00947-x

Z. Akridge, Z. Bradshaw

引用次数: 0

Large Time Behavior for the 3D Navier-Stokes with Navier Boundary Conditions 具有Navier边界条件的三维Navier- stokes大时间行为

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-27 DOI: 10.1007/s00021-025-00951-1

James P. Kelliher, Christophe Lacave, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, Edriss S. Titi

{"title":"Large Time Behavior for the 3D Navier-Stokes with Navier Boundary Conditions","authors":"James P. Kelliher, Christophe Lacave, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, Edriss S. Titi","doi":"10.1007/s00021-025-00951-1","DOIUrl":"10.1007/s00021-025-00951-1","url":null,"abstract":"<div><p>We study the three-dimensional incompressible Navier-Stokes equations in a smooth bounded domain <span>(Omega )</span> with initial velocity <span>(u_0)</span> square-integrable, divergence-free and tangent to <span>(partial Omega )</span>. We supplement the equations with the Navier friction boundary conditions <span>(u cdot {varvec{n}}= 0)</span> and <span>([(2Su){varvec{n}}+ alpha u]_{{scriptstyle {textrm{tan}}}} = 0)</span>, where <span>({varvec{n}})</span> is the unit exterior normal to <span>(partial Omega )</span>, <span>(Su = (Du + (Du)^t)/2)</span>, <span>(alpha in C^0(partial Omega ))</span> is the boundary friction coefficient and <span>([cdot ]_{{scriptstyle {textrm{tan}}}})</span> is the projection of its argument onto the tangent space of <span>(partial Omega )</span>. We prove global existence of a weak Leray-type solution to the resulting initial-boundary value problem and exponential decay in energy norm of these solutions when friction is positive. We also prove exponential decay if friction is non-negative and the domain is not a solid of revolution. These two results are well known in the case of Dirichlet boundary condition, but, even if they have been implicitly used for the Navier boundary conditions, the comprehensive analysis is not available in the literature. After carefully studying the Stokes semigroup for such a boundary condition, we use the Galerkin method for existence, Poincaré-type inequalities, with suitable adaptations to account for the differential geometry of the boundary, and a novel integral Gronwall-type inequality. In addition, in the frictionless case <span>(alpha = 0)</span>, we prove convergence of the solution to a steady rigid rotation, if the domain is a solid of revolution.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170668","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}

引用次数: 0

A Single Peaked Solitary Wave Solution of the Modified Camassa-Holm-Kadomtsev-Petviashvili Equation 修正Camassa-Holm-Kadomtsev-Petviashvili方程的单峰孤波解

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-27 DOI: 10.1007/s00021-025-00953-z

Byungsoo Moon

引用次数: 0

A Well-Posedness Result for the Compressible Two-Fluid Model with Density-Dependent Viscosity 黏度随密度变化的可压缩双流体模型的适定性结果

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-27 DOI: 10.1007/s00021-025-00954-y

Sagbo Marcel Zodji

引用次数: 0

Thermal Convection in a Higher Velocity Gradient and Higher Temperature Gradient Fluid 高速度梯度和高温度梯度流体中的热对流

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-20 DOI: 10.1007/s00021-025-00950-2

Giulia Giantesio, Alberto Girelli, Chiara Lonati, Alfredo Marzocchi, Alessandro Musesti, Brian Straughan

{"title":"Thermal Convection in a Higher Velocity Gradient and Higher Temperature Gradient Fluid","authors":"Giulia Giantesio, Alberto Girelli, Chiara Lonati, Alfredo Marzocchi, Alessandro Musesti, Brian Straughan","doi":"10.1007/s00021-025-00950-2","DOIUrl":"10.1007/s00021-025-00950-2","url":null,"abstract":"<div><p>We analyse a model for thermal convection in a class of generalized Navier-Stokes equations containing fourth order spatial derivatives of the velocity and of the temperature. The work generalises the isothermal model of A. Musesti. We derive critical Rayleigh and wavenumbers for the onset of convective fluid motion paying careful attention to the variation of coefficients of the highest derivatives. In addition to linear instability theory we include an analysis of fully nonlinear stability theory. The theory analysed possesses a bi-Laplacian term for the velocity field and also for the temperature field. It was pointed out by E. Fried and M. Gurtin that higher order terms represent micro-length effects and these phenomena are very important in flows in microfluidic situations. We introduce temperature into the theory via a Boussinesq approximation where the density of the body force term is allowed to depend upon temperature to account for buoyancy effects which arise due to expansion of the fluid when this is heated. We analyse a meaningful set of boundary conditions which are introduced by Fried and Gurtin as conditions of strong adherence, and these are crucial to understand the effect of the higher order derivatives upon convective motion in a microfluidic scenario where micro-length effects are paramount. The basic steady state is the one of zero velocity, but in contrast to the classical theory the temperature field is nonlinear in the vertical coordinate. This requires care especially dealing with nonlinear theory and also leads to some novel effects.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167533","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}

引用次数: 0

Partial Regularity for the Steady Fractional Navier-Stokes Equations in Dimension (mathbf{{n}}) 稳定分数阶Navier-Stokes方程的部分正则性 (mathbf{{n}})

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-18 DOI: 10.1007/s00021-025-00952-0

Jiaqi Yang

引用次数: 0