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The Regularity Criterion to the Navier–Stokes Equations Based on One Entry of the Velocity Gradient 基于速度梯度单入口的Navier-Stokes方程的正则性判据
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-01-05 DOI: 10.1007/s00021-025-00995-3
Khadijeh Baghaei
{"title":"The Regularity Criterion to the Navier–Stokes Equations Based on One Entry of the Velocity Gradient","authors":"Khadijeh Baghaei","doi":"10.1007/s00021-025-00995-3","DOIUrl":"10.1007/s00021-025-00995-3","url":null,"abstract":"<div><p>In this paper, we present a regularity criterion to the Navier–Stokes equations based on one entry of the velocity gradient. In fact, we prove that the weak solution to the Navier-Stokes equations is regular provided that <span>(partial _{3}u_{3}in L^{beta }(0, T; L^{alpha }(mathbb {R} ^{3})))</span> with <span>(alpha &gt;frac{7+sqrt{13}}{6})</span> and: </p><div><div><span>$$begin{aligned} frac{2}{beta }+frac{3}{alpha }= frac{-12,widehat{alpha }^{2}+28, widehat{alpha }-3+sqrt{ (3-2, widehat{alpha })(-72,widehat{alpha }^{3}+276, widehat{alpha }^{2}-374,widehat{alpha }+195)}}{8(2-widehat{alpha })}, end{aligned}$$</span></div></div><p>where <span>( widehat{alpha }=frac{1}{alpha }.)</span> This result improves the previous result obtained by Zujin Zhang and Yali Zhang in (Z. Angew. Math. Phys.)(2021), which states the similar result for <span>(alpha ge frac{3+sqrt{17}}{4}.)</span> Notice that <span>(frac{7+sqrt{13}}{6}&lt;frac{3+sqrt{17}}{4},)</span> thus the range of <span>(alpha )</span> is changed. Also, we show that <span>(beta )</span> corresponding to <span>(alpha )</span> which is obtained in our result is smaller than <span>(beta )</span> obtained in the mentioned paper.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929931","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
On a Generalized System with Applications to Ideal Magnetohydrodynamics 理想磁流体力学中的一个广义系统
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-01-04 DOI: 10.1007/s00021-025-00993-5
Alejandro Sarria
{"title":"On a Generalized System with Applications to Ideal Magnetohydrodynamics","authors":"Alejandro Sarria","doi":"10.1007/s00021-025-00993-5","DOIUrl":"10.1007/s00021-025-00993-5","url":null,"abstract":"<div><p>Finite-time blowup of solutions (<i>u</i>(<i>x</i>, <i>t</i>), <i>b</i>(<i>x</i>, <i>t</i>)) to a generalized system of equations with applications to ideal Magnetohydrodynamics (MHD) and one-dimensional fluid convection and stretching, among other areas, is investigated. The system is parameter-dependent, our spatial domain is the unit interval or the circle, and the initial data <span>((u_0(x),b_0(x)))</span> is assumed to be smooth. Among other results, we derive precise blowup criteria for specific values of the parameters by tracking the evolution of <span>(u_x)</span> along Lagrangian trajectories that originate at a point <span>(x_0)</span> at which <span>(b_0(x))</span> and <span>(b_0'(x))</span> vanish. We employ concavity arguments, energy estimates, and ODE comparison methods. We also show that for some values of the parameters, a non-vanishing <span>(b_0'(x_0))</span> suppresses finite-time blowup.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145929846","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
Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions 具有相变的两相流的扩散界面模型：建模和弱解的存在性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-12-26 DOI: 10.1007/s00021-025-00986-4
Helmut Abels, Harald Garcke, Julia Wittmann
{"title":"Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions","authors":"Helmut Abels,&nbsp;Harald Garcke,&nbsp;Julia Wittmann","doi":"10.1007/s00021-025-00986-4","DOIUrl":"10.1007/s00021-025-00986-4","url":null,"abstract":"<div><p>The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two quasi-incompressible diffuse interface models with singular free energies are analyzed, differing primarily in their velocity averaging. Firstly, to generalize a model by Abels, Garcke, and Grün, a thermodynamically consistent system of Navier–Stokes/Cahn–Hilliard type with source terms is derived in a framework of continuum fluid dynamics, followed by a proof of existence of weak solutions to the latter. Secondly, the quasi-stationary version of a model by Aki, Dreyer, Giesselmann, and Kraus is investigated analytically, with existence of weak solutions being established for the resulting quasi-stationary Stokes system coupled to a Cahn–Hilliard equation with a source term.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00986-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145831463","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
Stability of Partially Congested Travelling Wave Solutions for the Dissipative Aw-Rascle System 耗散Aw-Rascle系统部分拥挤行波解的稳定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-12-18 DOI: 10.1007/s00021-025-00988-2
É Deléage, Muhammed Ali Mehmood
{"title":"Stability of Partially Congested Travelling Wave Solutions for the Dissipative Aw-Rascle System","authors":"É Deléage,&nbsp;Muhammed Ali Mehmood","doi":"10.1007/s00021-025-00988-2","DOIUrl":"10.1007/s00021-025-00988-2","url":null,"abstract":"<div><p>We prove the non-linear stability of a class of travelling-wave solutions to the dissipative Aw-Rascle system with a singular offset function, which is formally equivalent to the compressible pressureless Navier-Stokes system with a singular viscosity. These solutions encode the effect of congestion by connecting a congested left state to an uncongested right state, and may also be viewed as approximations of solutions to the ‘hard-congestion model’. By using carefully weighted energy estimates we are able to prove the non-linear stability of viscous shock waves to the Aw-Rascle system under a small zero integral perturbation, which in particular extends previous results that do not handle the case where the viscosity is singular.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00988-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145778672","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
Well-posedness of Entropy-Bounded Solutions to 3D Compressible Nematic Liquid Crystal Flows with Far Field Vacuum 远场真空下三维可压缩向列液晶流熵有界解的适定性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-12-13 DOI: 10.1007/s00021-025-00987-3
Qiang Tao, Yuxin Zhai
{"title":"Well-posedness of Entropy-Bounded Solutions to 3D Compressible Nematic Liquid Crystal Flows with Far Field Vacuum","authors":"Qiang Tao,&nbsp;Yuxin Zhai","doi":"10.1007/s00021-025-00987-3","DOIUrl":"10.1007/s00021-025-00987-3","url":null,"abstract":"<div><p>The kinetic behavior of the physical entropy of viscous and heat-conductive fluids is an important and challenging problem, since the entropy equation possesses high degeneracy and singularity in the vacuum region. This article presents a conclusion that for the heat-conductive compressible nematic liquid system, the strong solution to the Cauchy problem is uniformly bounded in entropy and the <span>(L^{2})</span> regularities of the velocity and temperature can be preserved, provided the initial density vanishes in the far field is less than <span>(O left( frac{1}{|x |^{2}}right) )</span>, which improved the previous work [18]. The proof relies on the singular weighted energy method and a modified De Giorgi type iterative technique.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145778770","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
Asymptotic Behavior of Solutions to Compressible Euler Equations with Time and Space Dependent Damping 具有时空相关阻尼的可压缩欧拉方程解的渐近性质
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-12-05 DOI: 10.1007/s00021-025-00984-6
Nangao Zhang
{"title":"Asymptotic Behavior of Solutions to Compressible Euler Equations with Time and Space Dependent Damping","authors":"Nangao Zhang","doi":"10.1007/s00021-025-00984-6","DOIUrl":"10.1007/s00021-025-00984-6","url":null,"abstract":"<div><p>This paper is concerned with the asymptotic behavior of solutions to the Cauchy problem for 1D compressible Euler equations with damping of time and space dependent coefficient <span>(alpha (x,t))</span>, which models the compressible flow through porous media. We prove that the solutions to this system globally exist and converge to the diffusion waves, which are the self-similar solutions to the corresponding nonlinear parabolic equation given by Darcy’s law. The optimal convergence rates are also obtained. The proof is accomplished by virtue of energy estimates.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145675559","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
Zero-Viscosity Limit of the MHD Equations in the Mixed Prandtl-Shercliff Regime 混合Prandtl-Shercliff状态下MHD方程的零粘度极限
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-12-05 DOI: 10.1007/s00021-025-00982-8
Qi An, Zhan Xu
{"title":"Zero-Viscosity Limit of the MHD Equations in the Mixed Prandtl-Shercliff Regime","authors":"Qi An,&nbsp;Zhan Xu","doi":"10.1007/s00021-025-00982-8","DOIUrl":"10.1007/s00021-025-00982-8","url":null,"abstract":"<div><p>In this paper, we study the zero-viscosity limit of the two-dimensional MHD equations in the mixed Prandtl-Shercliff regime. Under the assumption that the initial tangential magnetic field is a non-zero constant, we justify the zero-viscosity limit for Sobolev initial data and obtain the optimal convergence rate in <span>({L}^{infty })</span> space.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145675558","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
The Zero-Mach Limit of Compressible Navier-Stokes Equations in Bounded Domains with Non-slip Boundary Condition 具有无滑移边界条件的有界区域上可压缩Navier-Stokes方程的零马赫极限
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-11-17 DOI: 10.1007/s00021-025-00981-9
Xinyu Fan, Qiangchang Ju, Jianjun Xu
{"title":"The Zero-Mach Limit of Compressible Navier-Stokes Equations in Bounded Domains with Non-slip Boundary Condition","authors":"Xinyu Fan,&nbsp;Qiangchang Ju,&nbsp;Jianjun Xu","doi":"10.1007/s00021-025-00981-9","DOIUrl":"10.1007/s00021-025-00981-9","url":null,"abstract":"<div><p>We investigate the zero-Mach limit of compressible Navier-Stokes equations in 3D bounded domains with non-slip boundary condition. No smallness restrictions are imposed on the initial velocity and the time interval. If the limiting system admits a reasonably smooth solution on a certain period, we verify that the corresponding compressible system admits the smooth solution on the same duration as well, provided the Mach number is small enough. Moreover, the solutions of compressible system converge uniformly to that of the incompressible one as Mach number tends to zero. We apply the global geometric tools introduced by Chrisrodoulou-Lindblad [8] to get higher order estimates of the density near the boundary, which also help us relax the smallness condition <span>(Vert nabla ^2rho _0Vert le Cvarepsilon )</span> in previous works to <span>(Vert nabla ^2rho _0Vert le Cvarepsilon ^{-alpha })</span> for some <span>(alpha ge 0)</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145561349","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
Existence of Non-Decaying Solutions to the Generalized Surface Quasi-Geostrophic Equations 广义曲面拟地转方程非衰减解的存在性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-11-12 DOI: 10.1007/s00021-025-00980-w
Zachary Radke
{"title":"Existence of Non-Decaying Solutions to the Generalized Surface Quasi-Geostrophic Equations","authors":"Zachary Radke","doi":"10.1007/s00021-025-00980-w","DOIUrl":"10.1007/s00021-025-00980-w","url":null,"abstract":"<div><p>We establish the short-time existence and uniqueness of non-decaying solutions to the generalized Surface Quasi-Geostrophic equations in Hölder-Zygmund spaces <span>(C^r(mathbb {R}^2))</span> for <span>(r&gt;1)</span> and uniformly local Sobolev spaces <span>(H_{ul}^s(mathbb {R}^2))</span> for <span>(s&gt;2)</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145493474","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
The Motion of a Rigid Body in a Viscous Fluid: Results for Strong Solutions, Uniqueness and Integrability Properties 粘性流体中刚体的运动：强解的结果，唯一性和可积性
IF 1.3 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2025-10-27 DOI: 10.1007/s00021-025-00977-5
Paolo Maremonti, Filippo Palma
{"title":"The Motion of a Rigid Body in a Viscous Fluid: Results for Strong Solutions, Uniqueness and Integrability Properties","authors":"Paolo Maremonti,&nbsp;Filippo Palma","doi":"10.1007/s00021-025-00977-5","DOIUrl":"10.1007/s00021-025-00977-5","url":null,"abstract":"<div><p>In this note, we show two results in the setting of Galdi-Silvestre strong solutions for the rigid body-viscous fluid interaction. The former, under an additional integrability assumption on the gradient of the initial datum, proves that the time derivative of the solution belongs to <span>(L^2(0,T;L^2(Omega )))</span>. The latter, thanks to a further assumption only on one solution, proves that the uniqueness holds in the quoted setting. However, our extra assumption for the uniqueness is certainly verified under the integrability assumption on the gradient of the initial datum. Hence, the set of solutions enjoying the uniqueness is not empty.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-025-00977-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145406003","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
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