Journal of Mathematical Fluid Mechanics最新文献_第4页

Fractional Voigt-Regularization of the 3D Navier–Stokes and Euler Equations: Global Well-Posedness and Limiting Behavior 三维Navier-Stokes和Euler方程的分数voight正则化：全局适定性和极限行为

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-09 DOI: 10.1007/s00021-025-00948-w

Zdzisław Brzeźniak, Adam Larios, Isabel Safarik

{"title":"Fractional Voigt-Regularization of the 3D Navier–Stokes and Euler Equations: Global Well-Posedness and Limiting Behavior","authors":"Zdzisław Brzeźniak, Adam Larios, Isabel Safarik","doi":"10.1007/s00021-025-00948-w","DOIUrl":"10.1007/s00021-025-00948-w","url":null,"abstract":"<div>The Voigt regularization is a technique used to model turbulent flows, offering advantages such as sharing steady states with the Navier-Stokes equations and requiring no modification of boundary conditions; however, the parabolic dissipative character of the equation is lost. In this work we propose and study a generalization of the Voigt regularization technique by introducing a fractional power r in the Helmholtz operator, which allows for dissipation in the system, at least in the viscous case. We examine the resulting fractional Navier-Stokes-Voigt (fNSV) and fractional Euler-Voigt (fEV) and show that global well-posedness holds in the 3D periodic case for fNSV when the fractional power (r ge frac{1}{2}) and for fEV when (r>frac{5}{6}). Moreover, we show that the solutions of these fractional Voigt-regularized systems converge to solutions of the original equations, on the corresponding time interval of existence and uniqueness of the latter, as the regularization parameter (alpha rightarrow 0). Additionally, we prove convergence of solutions of fNSV to solutions of fEV as the viscosity (nu rightarrow 0) as well as the convergence of solutions of fNSV to solutions of the 3D Euler equations as both (alpha , nu rightarrow 0). Furthermore, we derive a criterion for finite-time blow-up for each system based on this regularization. These results may be of use to researchers in both pure and applied fluid dynamics, particularly in terms of approximate models for turbulence and as tools to investigate potential blow-up of solutions.</div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163987","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 Solutions and Asymptotic Behavior for the Three-dimensional Viscous Non-resistive MHD System with Some Large Perturbations 具有大扰动的三维粘性无阻力MHD系统的全局解和渐近行为

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-07 DOI: 10.1007/s00021-025-00949-9

Youyi Zhao

{"title":"Global Solutions and Asymptotic Behavior for the Three-dimensional Viscous Non-resistive MHD System with Some Large Perturbations","authors":"Youyi Zhao","doi":"10.1007/s00021-025-00949-9","DOIUrl":"10.1007/s00021-025-00949-9","url":null,"abstract":"<div>We revisit the global existence of solutions with some large perturbations to the incompressible, viscous, and non-resistive MHD system in a three-dimensional periodic domain, where the impressed magnetic field satisfies the Diophantine condition, and the intensity of the impressed magnetic field, denoted by m, is large compared to the perturbations. It was proved by Jiang–Jiang that the highest-order derivatives of the velocity increase with m and the convergence rate of the nonlinear system towards a linearized problem is of (m^{-1/2}) in [F. Jiang and S. Jiang, Arch. Ration. Mech. Anal., 247 (2023), 96]. In this paper, we adopt a different approach by leveraging vorticity estimates to establish the highest-order energy inequality. This strategy prevents the appearance of terms that grow with m, and thus the increasing behavior of the highest-order derivatives of the velocity with respect to m does not appear. Additionally, we use the vorticity estimates to demonstrate the convergence rate of the nonlinear system towards a linearized problem as time or m approaches infinity. Notably, our analysis reveals that the convergence rate in m is faster compared to the finding of Jiang–Jiang. Finally, a key contribution of our work is identifying an integrable time-decay of the lower-order dissipation. This finding can replace the time-decay of lower-order energy in closing the highest-order energy inequality, significantly relaxing the regularity requirements for the initial perturbations.</div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163294","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

Uniqueness of Mild Solutions to the Navier-Stokes Equations in Weak-type (L^d) Space 弱型(L^d)空间中Navier-Stokes方程温和解的唯一性

IF 1.3 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-06-02 DOI: 10.1007/s00021-025-00945-z

Zhirun Zhan

{"title":"Uniqueness of Mild Solutions to the Navier-Stokes Equations in Weak-type (L^d) Space","authors":"Zhirun Zhan","doi":"10.1007/s00021-025-00945-z","DOIUrl":"10.1007/s00021-025-00945-z","url":null,"abstract":"<div>This paper deals with the uniqueness of mild solutions to the forced or unforced Navier-Stokes equations in the whole space. It is known that the uniqueness of mild solutions to the unforced Navier-Stokes equations holds in (L^{infty }(0,T;L^d({mathbb {R}}^d))) when (dge 4), and in (C([0,T];L^d({mathbb {R}}^d))) when (dge 3). As for the forced Navier-Stokes equations, when (dge 3) the uniqueness of mild solutions in (C([0,T];L^{d,infty }({mathbb {R}}^d))) with force f and initial data (u_{0}) in appropriate Lorentz spaces is known. In this paper we show that for (dge 3), the uniqueness of mild solutions to the forced Navier-Stokes equations in ( C((0,T];{widetilde{L}}^{d,infty }({mathbb {R}}^d))cap L^beta (0,T;{widetilde{L}}^{d,infty }({mathbb {R}}^d))) for (beta >2d/(d-2)) holds when there is a mild solution in (C([0,T];{widetilde{L}}^{d,infty }({mathbb {R}}^d))) with the same initial data and force. Here ({widetilde{L}}^{d,infty }) is the closure of ({L^{infty }cap L^{d,infty }}) with respect to (L^{d,infty }) norm.</div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160938","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 the Effect of a Large Cloud of Rigid Particles on the Motion of an Incompressible Non–Newtonian Fluid 一大片刚性粒子云对不可压缩非牛顿流体运动的影响

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-25 DOI: 10.1007/s00021-025-00944-0

Eduard Feireisl, Arnab Roy, Arghir Zarnescu

引用次数: 0

Strong Convergence of Low Mach Number Limit for the Compressible Navier–Stokes Equations in the Scaling Critical Spaces 尺度临界空间中可压缩Navier-Stokes方程低马赫数极限的强收敛性

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-24 DOI: 10.1007/s00021-025-00938-y

Shozo Ogino

引用次数: 0

Temperature Dependent Precipitation in Exact Nonlinear Mountain Waves 精确非线性山波中的温度相关降水

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-24 DOI: 10.1007/s00021-025-00946-y

Tony Lyons, Jordan McCarney

引用次数: 0

Spectral Stability of Multi-Solitons for the Kaup-Kupershmidt Equation kup - kupershmidt方程多孤子的谱稳定性

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-14 DOI: 10.1007/s00021-025-00942-2

Zhong Wang

引用次数: 0

On the Pathwise Uniqueness of Stochastic 2D Euler Equations with Kraichnan Noise and (L^p)-data 具有Kraichnan噪声和(L^p) -数据的随机二维欧拉方程的路径唯一性

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-14 DOI: 10.1007/s00021-025-00943-1

Shuaijie Jiao, Dejun Luo

引用次数: 0

On Basic Velocity Estimates for the Plane Steady-State Navier–Stokes System and Its Applications 平面稳态Navier-Stokes系统的基本速度估计及其应用

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-10 DOI: 10.1007/s00021-025-00939-x

Mikhail Korobkov, Xiao Ren

引用次数: 0

On a Two-Component Shallow-Water Model with the Weak Coriolis and Equatorial Undercurrent Effects 具有弱科里奥利效应和赤道潜流效应的双分量浅水模式

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-09 DOI: 10.1007/s00021-025-00940-4

Lili Huang, Yaojun Yang, Shouming Zhou

{"title":"On a Two-Component Shallow-Water Model with the Weak Coriolis and Equatorial Undercurrent Effects","authors":"Lili Huang, Yaojun Yang, Shouming Zhou","doi":"10.1007/s00021-025-00940-4","DOIUrl":"10.1007/s00021-025-00940-4","url":null,"abstract":"<div>The present paper studies a two-component mathematical model representing shallow-water wave propagation primarily in equatorial ocean regions, incorporating the effects of weak Coriolis force and equatorial undercurrent. We start with the Green–Naghdi type equations under the weak Coriolis and equatorial undercurrent effects from the Euler equations, then the two-component Camassa–Holm system with the two effects is derived by truncating asymptotic expansions of the quantities to the appropriate order. Analytically, we study the mathematical properties of the solutions to the two-component Camassa–Holm system including the ill-posedness of the solutions in Besov spaces (B^{s}_{p,infty }times B^{s-1}_{p,infty }) with (1le ple infty ) and (s>max left{ 2+frac{1}{p},frac{5}{2}right} ), the Hölder continuity of the data-to-solution map in Besov spaces (B^{s}_{p,r}times B^{s-1}_{p,r}) with (1le p,rle infty ) and (s>max left{ 2+frac{1}{p},frac{5}{2}right} ). We then investigate the Gevrey regularity and analyticity of the system in ({G_{delta ,s}^{gamma }}times {G_{delta ,s-1}^{gamma }}) with (delta ge 1, nu>gamma >0) and (s>frac{5}{2}). Finally, we provide the persistence properties and the spatial asymptotic profiles of the solutions in weighted spaces (L ^ p_{phi }=L^p(mathbb {R},phi ^pdx)).</div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143925679","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