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

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

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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

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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>We study the three-dimensional incompressible Navier-Stokes equations in a smooth bounded domain (Omega ) with initial velocity (u_0) square-integrable, divergence-free and tangent to (partial Omega ). We supplement the equations with the Navier friction boundary conditions (u cdot {varvec{n}}= 0) and ([(2Su){varvec{n}}+ alpha u]_{{scriptstyle {textrm{tan}}}} = 0), where ({varvec{n}}) is the unit exterior normal to (partial Omega ), (Su = (Du + (Du)^t)/2), (alpha in C^0(partial Omega )) is the boundary friction coefficient and ([cdot ]_{{scriptstyle {textrm{tan}}}}) is the projection of its argument onto the tangent space of (partial Omega ). 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 (alpha = 0), we prove convergence of the solution to a steady rigid rotation, if the domain is a solid of revolution.</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}

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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

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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

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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>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.</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

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