Journal of Mathematical Fluid Mechanics最新文献

{"title":"Global Attractor and Singular Limits of the 3D Voigt-regularized Magnetohydrodynamic Equations","authors":"Xuesi Kong,&nbsp;Xingjie Yan,&nbsp;Rong Yang","doi":"10.1007/s00021-024-00909-9","DOIUrl":"10.1007/s00021-024-00909-9","url":null,"abstract":"<div><p>In this article, the 3D Voigt-regularized Magnetohydrodynamic equations are considered, for which it is unknown if the uniqueness of weak solution exists. First, we prove that the uniform global attractor exists by constructing an evolutionary system. Then singular limits of this system are established. Namely, when a certain regularization parameter disappears, the convergence of global attractors is shown between the 3D autonomous Voigt-regularized Magnetohydrodynamic equations and Magnetohydrodynamic equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142664416","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}

{"title":"Exact Solution and Instability for Saturn’s Stratified Circumpolar Atmospheric Flow","authors":"Jin Zhao,&nbsp;Xun Wang","doi":"10.1007/s00021-024-00906-y","DOIUrl":"10.1007/s00021-024-00906-y","url":null,"abstract":"<div><p>In this paper, we present an exact solution for the nonlinear governing equation coupled with relevant boundary conditions, which arise from the study of Saturn’s stratified circumpolar atmospheric flow. The solution is explicit in the Lagrangian framework by specifying its hypotrochoidal particle paths. An instability result of such nonlinear waves is also obtained by means of the short-wavelength instability approach.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636663","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}

{"title":"The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System","authors":"Shengbin Fu,&nbsp;Weiwei Wang","doi":"10.1007/s00021-023-00820-9","DOIUrl":"10.1007/s00021-023-00820-9","url":null,"abstract":"<div><p>In this paper, we are interested in the global well-posedness of the strong solutions to the Cauchy problem on the compressible magnetohydrodynamics system with Hall effect. Moreover, we establish the convergence rates of the above solutions trending towards the constant equilibrium <span>(({bar{rho }},0,bar{textbf{B}}))</span>, provided that the initial perturbation belonging to <span>(H^3({mathbb {R}}^3) cap B_{2, infty }^{-s}({mathbb {R}}^3))</span> for <span>(s in (0,frac{3}{2}])</span> is sufficiently small.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4996997","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}

{"title":"Global existence and optimal decay rates for a generic non--conservative compressible two--fluid model","authors":"Yin Li,&nbsp;Huaqiao Wang,&nbsp;Guochun Wu,&nbsp;Yinghui Zhang","doi":"10.1007/s00021-023-00822-7","DOIUrl":"10.1007/s00021-023-00822-7","url":null,"abstract":"<div><p>We investigate global existence and optimal decay rates of a generic non-conservative compressible two–fluid model with general constant viscosities and capillary coefficients, and our main purpose is three–fold: First, for any integer <span>(ell ge 3)</span>, we show that the densities and velocities converge to their corresponding equilibrium states at the <span>(L^2)</span> rate <span>((1+t)^{-frac{3}{4}})</span>, and the <i>k</i>(<span>(in [1, ell ])</span>)–order spatial derivatives of them converge to zero at the <span>(L^2)</span> rate <span>((1+t)^{-frac{3}{4}-frac{k}{2}})</span>, which are the same as ones of the compressible Navier–Stokes–Korteweg system. This can be regarded as non-straightforward generalization from the compressible Navier–Stokes–Korteweg system to the two–fluid model. Compared to the compressible Navier–Stokes–Korteweg system, many new mathematical challenges occur since the corresponding model is non-conservative, and its nonlinear structure is very terrible, and the corresponding linear system cannot be diagonalizable. One of key observations here is that to tackle with the strongly coupling terms, we will introduce the linear combination of the fraction densities (<span>(beta ^+alpha ^+rho ^++beta ^-alpha ^-rho ^-)</span>), and explore its good regularity, which is particularly better than ones of two fraction densities (<span>(alpha ^pm rho ^pm )</span>) themselves. Second, the linear combination of the fraction densities (<span>(beta ^+alpha ^+rho ^++beta ^-alpha ^-rho ^-)</span>) converges to its corresponding equilibrium state at the <span>(L^2)</span> rate <span>((1+t)^{-frac{3}{4}})</span>, and its <i>k</i>(<span>(in [1, ell ])</span>)–order spatial derivative converges to zero at the <span>(L^2)</span> rate <span>((1+t)^{-frac{3}{4}-frac{k}{2}})</span>, but the fraction densities (<span>(alpha ^pm rho ^pm )</span>) themselves converge to their corresponding equilibrium states at the <span>(L^2)</span> rate <span>((1+t)^{-frac{1}{4}})</span>, and the <i>k</i>(<span>(in [1, ell ])</span>)–order spatial derivatives of them converge to zero at the <span>(L^2)</span> rate <span>((1+t)^{-frac{1}{4}-frac{k}{2}})</span>, which are slower than ones of their linear combination (<span>(beta ^+alpha ^+rho ^++beta ^-alpha ^-rho ^-)</span>) and the densities. We think that this phenomenon should owe to the special structure of the system. Finally, for well–chosen initial data, we also prove the lower bounds on the decay rates, which are the same as those of the upper decay rates. Therefore, these decay rates are optimal for the compressible two–fluid model.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4961206","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}

{"title":"Localized Blow-Up Criterion for ( C^{ 1, alpha } ) Solutions to the 3D Incompressible Euler Equations","authors":"Dongho Chae,&nbsp;Jörg Wolf","doi":"10.1007/s00021-023-00813-8","DOIUrl":"10.1007/s00021-023-00813-8","url":null,"abstract":"<div><p>We prove a localized Beale–Kato–Majda type blow-up criterion for the 3D incompressible Euler equations in the Hölder space setting. More specifically, let <span>(vin C([0, T); C^{ 1, alpha } (Omega ))cap L^infty (0, T; L^2(Omega )))</span> be a solution to the Euler equations in a domain <span>(Omega subset {mathbb {R}}^3)</span>. If there exists a ball <span>(Bsubset Omega )</span> such that <span>( int limits nolimits _{0}^T Vert omega (s)Vert _{ BMO(B )} ds &lt; +infty , )</span> where <span>( omega = nabla times v)</span> stands for the vorticity, then <span>( vin C([0, T]; C^{ 1, alpha } (K)) )</span> for every compact subset <span>( K subset B )</span>. In the proof of this result, in order to handle the time evolution of the local Hölder norm of the vorticity we use the well-known Campanato space representation for the the Hölder space, and our argument relies on the Campanato space estimates for the solution to the corresponding transport equation.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4752455","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}

{"title":"Global Boundedness to a 3D Chemotaxis–Stokes System with Porous Medium Cell Diffusion and General Sensitivity Under Dirichlet Signal Boundary Condition","authors":"Yu Tian,&nbsp;Zhaoyin Xiang","doi":"10.1007/s00021-023-00812-9","DOIUrl":"10.1007/s00021-023-00812-9","url":null,"abstract":"<div><p>In this paper, we construct a globally bounded weak solution for the initial-boundary value problem of a three-dimensional chemotaxis–Stokes system with porous medium cell diffusion <span>(Delta n^m)</span> and inhomogeneous Dirichlet signal boundary for each <span>(m&gt;frac{13}{12})</span>. Compared with the quite well-developed solvability for the no-flux signal boundary value with <span>(m&gt;frac{7}{6})</span> (Winkler in Calc Var 54:3789–3828, 2015), to our best knowledge, this seems to be the first result on chemotaxis–fluid system with general matrix-valued sensitivity for such a Dirichlet signal boundary condition, under which even for the scalar sensitivity, we also extend the recent range <span>(m&gt;frac{7}{6})</span> (Wu and Xiang in J Differ Equ 315:122–158, 2022). Our proof will be based on a new observation on the boundary estimate and on a three-step induction argument. The same technique can be applied to the two-dimensional setting to confirm a similar conclusion for any <span>(m&gt;1)</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00812-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4391322","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}

{"title":"Spatially Quasi-Periodic Solutions of the Euler Equation","authors":"Xu Sun,&nbsp;Peter Topalov","doi":"10.1007/s00021-023-00804-9","DOIUrl":"10.1007/s00021-023-00804-9","url":null,"abstract":"<div><p>We develop a framework for studying quasi-periodic maps and diffeomorphisms on <span>({mathbb {R}}^n)</span>. As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on <span>({mathbb {R}}^n)</span>. In particular, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and the initial data are proved.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00804-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5151221","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}

{"title":"Two-Phase Flows with Bulk–Surface Interaction: Thermodynamically Consistent Navier–Stokes–Cahn–Hilliard Models with Dynamic Boundary Conditions","authors":"Andrea Giorgini,&nbsp;Patrik Knopf","doi":"10.1007/s00021-023-00811-w","DOIUrl":"10.1007/s00021-023-00811-w","url":null,"abstract":"<div><p>We derive a novel thermodynamically consistent Navier–Stokes–Cahn–Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous models in the literature, our new model allows for surface diffusion, a variable contact angle between the diffuse interface and the boundary, and mass transfer between bulk and surface. In particular, this transfer of material is subject to a mass conservation law including both a bulk and a surface contribution. The derivation is carried out by means of local energy dissipation laws and the Lagrange multiplier approach. Next, in the case of fluids with matched densities, we show the existence of global weak solutions in two and three dimensions as well as the uniqueness of weak solutions in two dimensions.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00811-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5482625","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}

{"title":"On the Design of Global-in-Time Newton-Multigrid-Pressure Schur Complement Solvers for Incompressible Flow Problems","authors":"Christoph Lohmann,&nbsp;Stefan Turek","doi":"10.1007/s00021-023-00807-6","DOIUrl":"10.1007/s00021-023-00807-6","url":null,"abstract":"<div><p>In this work, a new global-in-time solution strategy for incompressible flow problems is presented, which highly exploits the pressure Schur complement (PSC) approach for the construction of a space–time multigrid algorithm. For linear problems like the incompressible Stokes equations discretized in space using an inf-sup-stable finite element pair, the fundamental idea is to block the linear systems of equations associated with individual time steps into a single all-at-once saddle point problem for all velocity and pressure unknowns. Then the pressure Schur complement can be used to eliminate the velocity fields and set up an implicitly defined linear system for all pressure variables only. This algebraic manipulation allows the construction of parallel-in-time preconditioners for the corresponding all-at-once Picard iteration by extending frequently used sequential PSC preconditioners in a straightforward manner. For the construction of efficient solution strategies, the so defined preconditioners are employed in a GMRES method and then embedded as a smoother into a space–time multigrid algorithm, where the computational complexity of the coarse grid problem highly depends on the coarsening strategy in space and/or time. While commonly used finite element intergrid transfer operators are used in space, tailor-made prolongation and restriction matrices in time are required due to a special treatment of the pressure variable in the underlying time discretization. The so defined all-at-once multigrid solver is extended to the solution of the nonlinear Navier–Stokes equations by using Newton’s method for linearization of the global-in-time problem. In summary, the presented multigrid solution strategy only requires the efficient solution of time-dependent linear convection–diffusion–reaction equations and several independent Poisson-like problems. In order to demonstrate the potential of the proposed solution strategy for viscous fluid simulations with large time intervals, the convergence behavior is examined for various linear and nonlinear test cases.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00807-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5010235","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}

{"title":"Convergence of the Fully Discrete Incremental Projection Scheme for Incompressible Flows","authors":"T. Gallouët,&nbsp;R. Herbin,&nbsp;J. C. Latché,&nbsp;D. Maltese","doi":"10.1007/s00021-023-00810-x","DOIUrl":"10.1007/s00021-023-00810-x","url":null,"abstract":"<div><p>The present paper addresses the convergence of a first-order in time incremental projection scheme for the time-dependent incompressible Navier–Stokes equations to a weak solution. We prove the convergence of the approximate solutions obtained by a semi-discrete scheme and a fully discrete scheme using a staggered finite volume scheme on non uniform rectangular meshes. Some first a priori estimates on the approximate solutions yield their existence. Compactness arguments, relying on these estimates, together with some estimates on the translates of the discrete time derivatives, are then developed to obtain convergence (up to the extraction of a subsequence), when the time step tends to zero in the semi-discrete scheme and when the space and time steps tend to zero in the fully discrete scheme; the approximate solutions are thus shown to converge to a limit function which is then shown to be a weak solution to the continuous problem by passing to the limit in these schemes.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5010246","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}