Journal of Mathematical Fluid Mechanics最新文献_第2页

Uniform (L^p) Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing 非均质二维纳维-斯托克斯方程组解的均匀 $$L^p$$ 估计数及其在具有局部感应的趋化-流体系统中的应用

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-09-16 DOI: 10.1007/s00021-024-00899-8

Mario Fuest, Michael Winkler

{"title":"Uniform (L^p) Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing","authors":"Mario Fuest, Michael Winkler","doi":"10.1007/s00021-024-00899-8","DOIUrl":"10.1007/s00021-024-00899-8","url":null,"abstract":"<div><p>The chemotaxis-Navier–Stokes system </p><div><div><span>$$begin{aligned} left{ begin{array}{rcl} n_t+ucdot nabla n & =& Delta big (n c^{-alpha } big ), c_t+ ucdot nabla c & =& Delta c -nc, u_t + (ucdot nabla ) u & =& Delta u+nabla P + nnabla Phi , qquad nabla cdot u=0, end{array} right. end{aligned}$$</span></div></div><p>modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain <span>(Omega subset mathbb R^2)</span>. For all <span>(alpha > 0)</span> and all sufficiently regular <span>(Phi )</span>, we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for <i>u</i> at a point in the proof when knowledge about <i>n</i> is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time <span>(L^p)</span> estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time <span>(L^2)</span> norm of the force term raised to an arbitrary small power.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00899-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264117","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

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-09-05 DOI: 10.1007/s00021-024-00897-w

Wancheng Sheng, Yang Zhou

引用次数: 0

TKE Model Involving the Distance to the Wall—Part 1: The Relaxed Case 与墙壁距离有关的 TKE 模型--第 1 部分：松弛情况

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-09-02 DOI: 10.1007/s00021-024-00895-y

Cherif Amrouche, Guillaume Leloup, Roger Lewandowski

引用次数: 0

Stability for a System of the 2D Incompressible MHD Equations with Fractional Dissipation 具有分数耗散的二维不可压缩多流体力学方程系统的稳定性

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-08-29 DOI: 10.1007/s00021-024-00892-1

Wen Feng, Weinan Wang, Jiahong Wu

引用次数: 0

On the Support of Anomalous Dissipation Measures 论异常耗散度量的支持

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-08-22 DOI: 10.1007/s00021-024-00894-z

Luigi De Rosa, Theodore D. Drivas, Marco Inversi

{"title":"On the Support of Anomalous Dissipation Measures","authors":"Luigi De Rosa, Theodore D. Drivas, Marco Inversi","doi":"10.1007/s00021-024-00894-z","DOIUrl":"10.1007/s00021-024-00894-z","url":null,"abstract":"<div><p>By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of a physical boundary. Boundary dissipation, which can occur at both the time and the spatial boundary, is analyzed by suitably modifying the Duchon & Robert interior distributional approach. One implication of our results is that any bounded Euler solution (compressible or incompressible) arising as a zero viscosity limit of Navier–Stokes solutions cannot have anomalous dissipation supported on a set of dimension smaller than that of the space. This result is sharp, as demonstrated by entropy-producing shock solutions of compressible Euler (Drivas and Eyink in Commun Math Phys 359(2):733–763, 2018. https://doi.org/10.1007/s00220-017-3078-4; Majda in Am Math Soc 43(281):93, 1983. https://doi.org/10.1090/memo/0281) and by recent constructions of dissipative incompressible Euler solutions (Brue and De Lellis in Commun Math Phys 400(3):1507–1533, 2023. https://doi.org/10.1007/s00220-022-04626-0 624; Brue et al. in Commun Pure App Anal, 2023), as well as passive scalars (Colombo et al. in Ann PDE 9(2):21–48, 2023. https://doi.org/10.1007/s40818-023-00162-9; Drivas et al. in Arch Ration Mech Anal 243(3):1151–1180, 2022. https://doi.org/10.1007/s00205-021-01736-2). For <span>(L^q_tL^r_x)</span> suitable Leray–Hopf solutions of the <span>(d-)</span>dimensional Navier–Stokes equation we prove a bound of the dissipation in terms of the Parabolic Hausdorff measure <span>(mathcal {P}^{s})</span>, which gives <span>(s=d-2)</span> as soon as the solution lies in the Prodi–Serrin class. In the three-dimensional case, this matches with the Caffarelli–Kohn–Nirenberg partial regularity.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00894-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180272","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

Remarks on the Stabilization of Large-Scale Growth in the 2D Kuramoto–Sivashinsky Equation 关于二维库拉莫托-西瓦申斯基方程中大规模增长的稳定性的评论

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-08-21 DOI: 10.1007/s00021-024-00890-3

Adam Larios, Vincent R. Martinez

{"title":"Remarks on the Stabilization of Large-Scale Growth in the 2D Kuramoto–Sivashinsky Equation","authors":"Adam Larios, Vincent R. Martinez","doi":"10.1007/s00021-024-00890-3","DOIUrl":"10.1007/s00021-024-00890-3","url":null,"abstract":"<div><p>In this article, some elementary observations are is made regarding the behavior of solutions to the two-dimensional curl-free Burgers equation which suggests the distinguished role played by the scalar divergence field in determining the dynamics of the solution. These observations inspire a new divergence-based regularity condition for the two-dimensional Kuramoto–Sivashinsky equation (KSE) that provides conceptual clarity to the nature of the potential blow-up mechanism for this system. The relation of this regularity criterion to the Ladyzhenskaya–Prodi–Serrin-type criterion for the KSE is also established, thus providing the basis for the development of an alternative framework of regularity criterion for this equation based solely on the low-mode behavior of its solutions. The article concludes by applying these ideas to identify a conceptually simple modification of KSE that yields globally regular solutions, as well as providing a straightforward verification of this regularity criterion to establish global regularity of solutions to the 2D Burgers–Sivashinsky equation. The proofs are direct, elementary, and concise.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180273","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 Spherically Symmetric Solutions to the Compressible Navier–Stokes Equation Towards Stationary Waves 可压缩纳维-斯托克斯方程球面对称解的渐近行为走向静止波

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-08-05 DOI: 10.1007/s00021-024-00885-0

Itsuko Hashimoto, Shinya Nishibata, Souhei Sugizaki

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Asymptotic Criticality of the Navier–Stokes Regularity Problem 纳维-斯托克斯正则问题的渐近临界性

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-07-27 DOI: 10.1007/s00021-024-00888-x

Zoran Grujić, Liaosha Xu

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Formation of Finite Time Singularity for Axially Symmetric Magnetohydrodynamic Waves in 3-D 轴对称磁流体动力波三维有限时间奇点的形成

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-07-20 DOI: 10.1007/s00021-024-00889-w

Lv Cai, Ning-An Lai

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Blowup Criterion for Viscous Non-baratropic Flows with Zero Heat Conduction Involving Velocity Divergence 涉及速度发散的零热传导粘性非各向同性流动的吹胀准则

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-07-15 DOI: 10.1007/s00021-024-00887-y

Yongfu Wang

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