Journal of Mathematical Fluid Mechanics最新文献

Existence Theorems for the Steady-State Navier–Stokes Equations with Nonhomogeneous Slip Boundary Conditions in Two-dimensional Multiply-Connected Bounded Domains 二维多重连接有界域中具有非均质滑动边界条件的稳态纳维-斯托克斯方程的存在定理

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-12-18 DOI: 10.1007/s00021-024-00907-x

Giovanni P. Galdi, Tatsuki Yamamoto

{"title":"Existence Theorems for the Steady-State Navier–Stokes Equations with Nonhomogeneous Slip Boundary Conditions in Two-dimensional Multiply-Connected Bounded Domains","authors":"Giovanni P. Galdi, Tatsuki Yamamoto","doi":"10.1007/s00021-024-00907-x","DOIUrl":"10.1007/s00021-024-00907-x","url":null,"abstract":"<div><p>We study the nonhomogeneous boundary value problem for the steady-state Navier–Stokes equations under the slip boundary conditions in two-dimensional multiply-connected bounded domains. Employing the approach of Korobkov-Pileckas-Russo (Ann. Math. 181(2), 769-807, 2015), we prove that this problem has a solution if the friction coefficient is sufficiently large compared with the kinematic viscosity constant and the curvature of the boundary. No additional assumption (other than the necessary requirement of zero total flux through the boundary) is imposed on the boundary data. We also show that such an assumption on the friction coefficient is redundant for the existence of a solution in the case when the fluxes across each connected component of the boundary are sufficiently small, or the domain and the given data satisfy certain symmetry conditions. The crucial ingredient of our proof is the fact that the total head pressure corresponding to the solution to the steady Euler equations takes a constant value on each connected component of the boundary.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142845051","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 Well-Posedness and Asymptotic Behavior of Strong Solutions to an Initial-Boundary Value Problem of 3D Full Compressible MHD Equations 三维全可压缩多流体力学方程初始边界值问题的全局好求和强解渐近行为

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-12-17 DOI: 10.1007/s00021-024-00915-x

Hao Xu, Hong Ye, Jianwen Zhang

{"title":"Global Well-Posedness and Asymptotic Behavior of Strong Solutions to an Initial-Boundary Value Problem of 3D Full Compressible MHD Equations","authors":"Hao Xu, Hong Ye, Jianwen Zhang","doi":"10.1007/s00021-024-00915-x","DOIUrl":"10.1007/s00021-024-00915-x","url":null,"abstract":"<div><p>This paper is concerned with an initial-boundary value problem of full compressible magnetohydrodynamics (MHD) equations on 3D bounded domains subject to non-slip boundary condition for velocity, perfectly conducting boundary condition for magnetic field, and homogeneous Dirichlet boundary condition for temperature. The global well-posedness of strong solutions with initial vacuum is established and the exponential decay estimates of the solutions are obtained, provided the initial total energy is suitably small. More interestingly, it is shown that for <span>(pin (3,6))</span>, the <span>(L^p)</span>-norm of the gradient of density remains uniformly bounded for all <span>(tge 0)</span>. This is in sharp contrast to that in (Chen et al. in Global well-posedness of full compressible magnetohydrodynamic system in 3D bounded domains with large oscillations and vacuum. arXiv:2208.04480, Li et al. in Global existence of classical solutions to full compressible Navier–Stokes equations with large oscillations and vacuum in 3D bounded domains. arXiv:2207.00441), where the exponential growth of the gradient of density in <span>(L^p)</span>-norm was explored.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826123","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

Energy Conservation for the Compressible Euler Equations and Elastodynamics

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-12-11 DOI: 10.1007/s00021-024-00913-z

Yulin Ye, Yanqing Wang

引用次数: 0

On the Solvability of Weak Transmission Problem in Unbounded Domains with Non-compact Boundaries

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-12-06 DOI: 10.1007/s00021-024-00914-y

Hirokazu Saito, Jiang Xu, Xin Zhang, Wendu Zhou

引用次数: 0

Long-Term Existence for Perturbed Multiple Gas Balls and Their Asymptotic Behavior

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-11-30 DOI: 10.1007/s00021-024-00912-0

Gerhard Ströhmer

引用次数: 0

Stratified Ocean Currents with Constant Vorticity 具有恒定涡度的分层洋流

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-11-28 DOI: 10.1007/s00021-024-00910-2

Ronald Quirchmayr

{"title":"Stratified Ocean Currents with Constant Vorticity","authors":"Ronald Quirchmayr","doi":"10.1007/s00021-024-00910-2","DOIUrl":"10.1007/s00021-024-00910-2","url":null,"abstract":"<div><p>We analyze vertically stratified three-dimensional oceanic flows under the assumption of constant vorticity. More precisely, these flows are governed by the <i>f</i>-plane approximation for the divergence-free incompressible Euler equations at arbitrary off-equatorial latitudes. A discontinuous stratification gives rise to a freely moving impermeable interface, which separates the two fluid layers of different constant densities; the fluid domain is bounded by a flat ocean bed and a free surface. It turns out that the constant vorticity assumption enforces almost trivial bounded solutions: the vertical fluid velocity vanishes everywhere; the horizontal velocity components are simple harmonic oscillators with Coriolis frequency <i>f</i> and independent of the spatial variables; the pressure is hydrostatic apart from sinusoidal oscillations in time; both the surface and interface are flat. To enable larger classes of solutions, we discuss a forcing method, which yields a characterization of steady stratified purely zonal currents with nonzero constant vorticity. Finally, we discuss the related viscous problem, which has no nontrivial bounded solutions.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00910-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142737031","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

Finite Difference Methods for Linear Transport Equations with Sobolev Velocity Fields 具有索波列速度场的线性传输方程的有限差分方法

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-11-27 DOI: 10.1007/s00021-024-00911-1

Kohei Soga

{"title":"Finite Difference Methods for Linear Transport Equations with Sobolev Velocity Fields","authors":"Kohei Soga","doi":"10.1007/s00021-024-00911-1","DOIUrl":"10.1007/s00021-024-00911-1","url":null,"abstract":"<div><p>DiPerna and Lions (Invent Math 98(3):511–547, 1989) established the existence and uniqueness results for weak solutions to linear transport equations with Sobolev velocity fields. Motivated by fluid mechanics, this paper provides mathematical analysis on two simple finite difference methods applied to linear transport equations on a bounded domain with divergence-free (unbounded) Sobolev velocity fields. The first method is based on a Lax-Friedrichs type explicit scheme with a generalized hyperbolic scale, where truncation of an unbounded velocity field and its measure estimate are implemented to ensure the monotonicity of the scheme; the method is <span>(L^p)</span>-strongly convergent in the class of DiPerna–Lions weak solutions. The second method is based on an implicit scheme with <span>(L^2)</span>-estimates, where the discrete Helmholtz–Hodge decomposition for discretized velocity fields plays an important role to ensure the divergence-free constraint in the discrete problem; the method is scale-free and <span>(L^2)</span>-strongly convergent in the class of DiPerna–Lions weak solutions. The key point for both of the methods is to obtain fine <span>(L^2)</span>-bounds of approximate solutions that tend to the norm of the exact solution given by DiPerna–Lions. Finally, the explicit scheme is applied to the case with smooth velocity fields from the viewpoint of the level-set method for sharp interfaces involving transport equations, where rigorous discrete approximation of level-sets and their geometric quantities is discussed.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714215","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

An Inverse Problem for Steady Supersonic Potential Flow Past a Bending Wall 稳定超音速势能流过弯曲壁的逆问题

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-11-25 DOI: 10.1007/s00021-024-00908-w

Ningning Li, Yongqian Zhang

引用次数: 0

Existence of Orthogonal Domain walls in Bénard-Rayleigh Convection 贝纳德-雷利对流中正交域壁的存在性

IF 1.2 3区数学

Journal of Mathematical Fluid Mechanics Pub Date : 2024-11-18 DOI: 10.1007/s00021-024-00891-2

Gérard Iooss

引用次数: 0

Global Attractor and Singular Limits of the 3D Voigt-regularized Magnetohydrodynamic Equations 三维 Voigt 规则化磁流体动力学方程的全局吸引和奇异极限