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On the Temporal Estimates for the Incompressible Navier-Stokes Equations and the Hall-magnetohydrodynamic Equations 不可压缩Navier-Stokes方程和hall -磁流体动力学方程的时间估计
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-07-15 DOI: 10.1007/s00021-026-01044-3
Hantaek Bae, Jinwook Jung, Jaeyong Shin
{"title":"On the Temporal Estimates for the Incompressible Navier-Stokes Equations and the Hall-magnetohydrodynamic Equations","authors":"Hantaek Bae,&nbsp;Jinwook Jung,&nbsp;Jaeyong Shin","doi":"10.1007/s00021-026-01044-3","DOIUrl":"10.1007/s00021-026-01044-3","url":null,"abstract":"<div><p>In this paper, we derive decay rates for solutions to the incompressible Navier-Stokes equations and Hall-magnetohydrodynamic equations. We first improve the decay rate of weak solutions to these equations by refining the Fourier splitting method with initial data in the space of pseudo-measures. Additionally, we investigate these equations with initial data in the Lei-Lin spaces and establish decay rates for those solutions.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466305","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 Priori Estimates of Plasma-Vacuum Interface Problem for 2D Incompressible Ideal MHD 二维不可压缩理想MHD等离子体-真空界面问题的先验估计
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-07-02 DOI: 10.1007/s00021-026-01032-7
Chengchun Hao
{"title":"A Priori Estimates of Plasma-Vacuum Interface Problem for 2D Incompressible Ideal MHD","authors":"Chengchun Hao","doi":"10.1007/s00021-026-01032-7","DOIUrl":"10.1007/s00021-026-01032-7","url":null,"abstract":"<div><p>This paper establishes a priori estimates for the free boundary problem of two-dimensional ideal incompressible magnetohydrodynamics (MHD) involving a plasma-vacuum interface. The system consists of a plasma region governed by the ideal MHD equations and a vacuum region described by pre-Maxwell dynamics, separated by a freely evolving interface where total pressure continuity and magnetic field tangency conditions hold. By adopting a geometric Lagrangian framework, we reformulate the free boundary problem into a fixed domain using trajectory maps and fictitious velocity extensions. Our main contribution lies in deriving higher-order energy norms that combine boundary geometry and interior dynamics, enabling control over the solution’s regularity. For the vacuum magnetic field, we prove that its covariant derivatives in <span>(L^2)</span> norms are bounded solely by initial data and curvature parameters, leveraging geometric trace inequalities under bounded curvature constraints. Additionally, we establish evolution equations for the electric field in vacuum and demonstrate energy exchanges between plasma and vacuum regions through pressure balance. The results provide a crucial step towards proving well-posedness for this challenging interface problem.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380616","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 Lagrangian Interior Regularity Result for the Incompressible Free Boundary Magnetohydrodynamics Equations with Surface Tension 具有表面张力的不可压缩自由边界磁流体动力学方程的拉格朗日内部正则性
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-07-01 DOI: 10.1007/s00021-026-01040-7
Zhi Chen, Weixun Feng, Dongdong Qin, Fan Wu
{"title":"A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Magnetohydrodynamics Equations with Surface Tension","authors":"Zhi Chen,&nbsp;Weixun Feng,&nbsp;Dongdong Qin,&nbsp;Fan Wu","doi":"10.1007/s00021-026-01040-7","DOIUrl":"10.1007/s00021-026-01040-7","url":null,"abstract":"<div><p>In this paper, we consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain involving a free moving surface boundary with surface tension. We derive the a priori estimate for solutions under minimal regularity assumptions on the initial data in Lagrangian coordinates. To the best of our knowledge, this seems to be the first attempt to establish the result of low regularity solution for incompressible free-boundary MHD equations with surface tension. Such result extends the works of Luo and Zhang [SIAM, 53 (2021), pp. 2595-2630] and Disconzi, Kukavica and Tuffaha [SIAM, 51 (2019), pp. 3982-4022].</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380581","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 Sharp Global Boundedness Result for Keller–Segel–(Navier–)Stokes Systems with Rapid Diffusion and Saturated Sensitivities 具有快速扩散和饱和灵敏度的Keller-Segel - (Navier -)Stokes系统的全局有界性
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-06-30 DOI: 10.1007/s00021-026-01041-6
Minh Le
{"title":"A Sharp Global Boundedness Result for Keller–Segel–(Navier–)Stokes Systems with Rapid Diffusion and Saturated Sensitivities","authors":"Minh Le","doi":"10.1007/s00021-026-01041-6","DOIUrl":"10.1007/s00021-026-01041-6","url":null,"abstract":"<div><p>We investigate the Keller–Segel–(Navier–)Stokes system posed in a smooth bounded domain <span>(Omega subset mathbb {R}^N)</span> with <span>(N = 2,3)</span>: </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} n_t + u cdot nabla n = Delta n - nabla cdot big ( n S(n)nabla c big ), u cdot nabla c = Delta c - c + n, u_t + kappa (u cdot nabla ) u = Delta u - nabla P + n nabla phi , nabla cdot u = 0, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(kappa in left{ 0,1 right} )</span>, the given gravitational potential <span>(phi in W^{2, infty }(Omega ))</span>, and the chemotactic sensitivity function <span>(S in C^2([0,infty )))</span>. Under no-flux boundary conditions for <span>(n)</span> and <span>(c)</span>, together with the Dirichlet boundary condition for <span>(u)</span>, we show that, provided the initial data satisfy suitable regularity assumptions, the following results hold:</p><ul>\u0000 <li>\u0000 <p>If <span>(N = 2)</span>, <span>(kappa = 1)</span>, and the sensitivity function satisfies <span>(lim _{xi rightarrow infty } S(xi ) = 0)</span>, then the Keller–Segel–Navier–Stokes system admits a global classical solution that remains uniformly bounded in time.</p>\u0000 </li>\u0000 <li>\u0000 <p>If <span>(N = 3)</span>, <span>(kappa = 0)</span>, and <span>(S)</span> satisfies </p><div><div><span>$$ |S(xi )| le K_S (xi + 1)^{-alpha } quad text {for all } xi ge 0, $$</span></div></div><p> with some constants <span>(K_S &gt; 0)</span> and <span>(alpha &gt; frac{1}{3})</span>, then the Keller–Segel–Stokes system possesses a global bounded classical solution.</p>\u0000 </li>\u0000 </ul><p> Our results expected to be optimal, since it is well established that, in the absence of fluid effects, blow-up can occur when <span>(S equiv textrm{const})</span> in two dimensions, or when <span>(alpha &lt; tfrac{1}{3})</span> in three dimensions.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148381076","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 Existence and Analyticity of the Equatorial Ocean Flow Model in Critical Besov Spaces 临界Besov空间中赤道海流模式的全局存在性和解析性
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-06-30 DOI: 10.1007/s00021-026-01036-3
Bingbing Dai, Zhen He, Wei Luo, Zhaoyang Yin
{"title":"Global Existence and Analyticity of the Equatorial Ocean Flow Model in Critical Besov Spaces","authors":"Bingbing Dai,&nbsp;Zhen He,&nbsp;Wei Luo,&nbsp;Zhaoyang Yin","doi":"10.1007/s00021-026-01036-3","DOIUrl":"10.1007/s00021-026-01036-3","url":null,"abstract":"<div><p>We study the Cauchy problem for a nonlocal evolution model arising in equatorial ocean flows. We prove global existence of solutions for small initial data in critical Besov spaces and show that these solutions become instantly spatially analytic. Our approach introduces exponentially weighted unknowns to capture the interplay between the dissipative linear operator and the nonlocal Hilbert transform, allowing precise control of the bilinear nonlinearity. This provides a unified framework to extend small-data global existence and analyticity results from classical fluid equations to a nonlocal dispersive-dissipative setting.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148381075","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
Thermohaline Convections in the Horizontal Layer with Non-Uniform Heat Supply 非均匀供热条件下的水平层温盐对流
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-06-25 DOI: 10.1007/s00021-026-01034-5
Hiroshi Fujiwara, Chun-Hsiung Hsia, Takaaki Nishida
{"title":"Thermohaline Convections in the Horizontal Layer with Non-Uniform Heat Supply","authors":"Hiroshi Fujiwara,&nbsp;Chun-Hsiung Hsia,&nbsp;Takaaki Nishida","doi":"10.1007/s00021-026-01034-5","DOIUrl":"10.1007/s00021-026-01034-5","url":null,"abstract":"<div><p>In this article, we study a thermohaline convection in horizontal fluid layer such that the gravity is considered. The fluid is heated from above non-uniformly. An existence theorem of stationary solutions is provided by a fixed point argument. Some interesting flow patterns are demonstrated by numerical computations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-026-01034-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323633","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
Large-Time Behavior of Global Solutions to the Cauchy Problem of the Planar Compressible Magnetohydrodynamic Equations 平面可压缩磁流体动力学方程Cauchy问题整体解的大时间行为
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-06-22 DOI: 10.1007/s00021-026-01037-2
Fang Li, Yongkai Liao, Ling Wan
{"title":"Large-Time Behavior of Global Solutions to the Cauchy Problem of the Planar Compressible Magnetohydrodynamic Equations","authors":"Fang Li,&nbsp;Yongkai Liao,&nbsp;Ling Wan","doi":"10.1007/s00021-026-01037-2","DOIUrl":"10.1007/s00021-026-01037-2","url":null,"abstract":"<div><p>There have already been some results concerning on the global existence of solutions to the Cauchy problem of the planar compressible magnetohydrodynamic equations with large initial data. However, few results have focused on its large-time behavior. The main purpose of this paper is to study the large-time behavior of global solutions to the Cauchy problem of the above system. The viscosity can be a positive constant or density-dependent. The key point in our analysis is to derive the uniform-in-time positive lower and upper bounds on the specific volume and the absolute temperature. Moreover, the interaction between the hydrodynamics and magnetodynamic effects has also been dealt with properly.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323488","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 the Hall Magnetohydrodynamic Model for Quantum Plasmas 量子等离子体霍尔磁流体力学模型的渐近行为
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-06-22 DOI: 10.1007/s00021-026-01038-1
Xiuli Xu, Xueke Pu
{"title":"Asymptotic Behavior of the Hall Magnetohydrodynamic Model for Quantum Plasmas","authors":"Xiuli Xu,&nbsp;Xueke Pu","doi":"10.1007/s00021-026-01038-1","DOIUrl":"10.1007/s00021-026-01038-1","url":null,"abstract":"<div><p>In this paper, we consider the quantum magnetohydrodynamic model for quantum plasmas. We first derive uniform estimates for the global smooth solutions in terms of the quantum coefficient <span>(hbar )</span> and the Hall coefficient <span>(epsilon )</span>. Then we establish the existence of global solutions and derive optimal convergence rates using the energy method. Next, applying the Lions-Aubin lemma, we prove that the unique smooth solution of the three-dimensional Hall-quantum-magnetohydrodynamic system converges globally in time to the smooth solution of the three-dimensional Navier-Stokes system as <span>(hbar )</span> and <span>(epsilon )</span> tend to zero. Furthermore, we provide the convergence rate estimates for any given positive time.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323490","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
Well-posedness for 2D Non-homogeneous Incompressible Fluids with General Density-Dependent Odd Viscosity 二维非均匀不可压缩流体的广义密度相关奇黏度的适定性
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-06-18 DOI: 10.1007/s00021-026-01024-7
Matthieu Pageard
{"title":"Well-posedness for 2D Non-homogeneous Incompressible Fluids with General Density-Dependent Odd Viscosity","authors":"Matthieu Pageard","doi":"10.1007/s00021-026-01024-7","DOIUrl":"10.1007/s00021-026-01024-7","url":null,"abstract":"<div><p>We study the initial value problem for a system of equations describing the motion of two-dimensional non-homogeneous incompressible fluids exhibiting odd (non-dissipative) viscosity effects. We consider the complete odd viscous stress tensor with a general density-dependent viscosity coefficient <span>(f(rho ))</span>. Under suitable assumptions, we prove the local existence and uniqueness of strong solutions in <span>({H^s}(mathbb {R}^2))</span> <span>((s&gt;2))</span>, for a class of viscosity coefficients covering the particular case <span>(f(rho )=arho ^alpha +b)</span> for any <span>((a,b,alpha )in mathbb {R}^3)</span>, generalising the result of [26] devoted to the case <span>(f(rho )=rho )</span>. Additionally, we are able to do so without requiring the initial density variation to belong to <span>({L^2}(mathbb {R}^2))</span>. As a major step of the proof, we exhibit an effective velocity for this sytem, generalising the so-called “Elsässer formulation” recently derived in [27].</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281069","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
Weak-Strong Uniqueness and the d’Alembert Paradox 弱-强唯一性和达朗贝尔悖论
IF 1.5 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2026-06-16 DOI: 10.1007/s00021-026-01033-6
Hao Quan, Gregory L. Eyink
{"title":"Weak-Strong Uniqueness and the d’Alembert Paradox","authors":"Hao Quan,&nbsp;Gregory L. Eyink","doi":"10.1007/s00021-026-01033-6","DOIUrl":"10.1007/s00021-026-01033-6","url":null,"abstract":"<div><p>We prove conditional weak-strong uniqueness of the potential Euler solution for external flow around a smooth body in three space dimensions, within the class of viscosity weak solutions with the same initial data. Our sufficient condition is the vanishing of the streamwise component of the skin friction integrated over the surface in the inviscid limit, slightly stronger than the condition of Kelliher and weakening that of Bardos-Titi, both for bounded domains. Because global-in-time existence of the smooth potential solution leads back to the d’Alembert paradox, we argue that weak-strong uniqueness is not a valid criterion for “relevant” notions of generalized Euler solution and that our condition is likely to be violated in the inviscid limit. We prove also that the Drivas-Nguyen condition on uniform continuity at the wall of the normal velocity component implies weak-strong uniqueness within the general class of admissible weak Euler solutions in bounded domains.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"28 3","pages":""},"PeriodicalIF":1.5,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281173","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
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