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Journal of Mathematical Fluid Mechanics最新文献

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Non-Uniqueness and Energy Dissipation for 2D Euler Equations with Vorticity in Hardy Spaces 哈代空间中带有涡性的二维欧拉方程的非唯一性和能量耗散
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-03-28 DOI: 10.1007/s00021-024-00860-9
Miriam Buck, Stefano Modena
{"title":"Non-Uniqueness and Energy Dissipation for 2D Euler Equations with Vorticity in Hardy Spaces","authors":"Miriam Buck,&nbsp;Stefano Modena","doi":"10.1007/s00021-024-00860-9","DOIUrl":"10.1007/s00021-024-00860-9","url":null,"abstract":"<div><p>We construct by convex integration examples of energy dissipating solutions to the 2D Euler equations on <span>({mathbb {R}}^2)</span> with vorticity in the Hardy space <span>(H^p({mathbb {R}}^2))</span>, for any <span>(2/3&lt;p&lt;1)</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00860-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315792","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
Augmented Lagrangian Acceleration of Global-in-Time Pressure Schur Complement Solvers for Incompressible Oseen Equations 针对不可压缩奥森方程的全局实时压力舒尔补全求解器的增量拉格朗日加速算法
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-03-28 DOI: 10.1007/s00021-024-00862-7
Christoph Lohmann, Stefan Turek
{"title":"Augmented Lagrangian Acceleration of Global-in-Time Pressure Schur Complement Solvers for Incompressible Oseen Equations","authors":"Christoph Lohmann,&nbsp;Stefan Turek","doi":"10.1007/s00021-024-00862-7","DOIUrl":"10.1007/s00021-024-00862-7","url":null,"abstract":"<div><p>This work is focused on an accelerated global-in-time solution strategy for the Oseen equations, which highly exploits the augmented Lagrangian methodology to improve the convergence behavior of the Schur complement iteration. The main idea of the solution strategy is to block the individual linear systems of equations at each time step into a single all-at-once saddle point problem. By elimination of all velocity unknowns, the resulting implicitly defined equation can then be solved using a global-in-time pressure Schur complement (PSC) iteration. To accelerate the convergence behavior of this iterative scheme, the augmented Lagrangian approach is exploited by modifying the momentum equation for all time steps in a strongly consistent manner. While the introduced discrete grad-div stabilization does not modify the solution of the discretized Oseen equations, the quality of customized PSC preconditioners drastically improves and, hence, guarantees a rapid convergence. This strategy comes at the cost that the involved auxiliary problem for the velocity field becomes ill conditioned so that standard iterative solution strategies are no longer efficient. Therefore, a highly specialized multigrid solver based on modified intergrid transfer operators and an additive block preconditioner is extended to solution of the all-at-once problem. The potential of the proposed overall solution strategy is discussed in several numerical studies as they occur in commonly used linearization techniques for the incompressible Navier–Stokes equations.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00862-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140315797","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
Blow-up Analysis for the ({varvec{ab}})-Family of Equations $${{varvec{ab}}$ -方程组的炸毁分析
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-24 DOI: 10.1007/s00021-024-00857-4
Wenguang Cheng, Ji Lin
{"title":"Blow-up Analysis for the ({varvec{ab}})-Family of Equations","authors":"Wenguang Cheng,&nbsp;Ji Lin","doi":"10.1007/s00021-024-00857-4","DOIUrl":"10.1007/s00021-024-00857-4","url":null,"abstract":"<div><p>This paper investigates the Cauchy problem for the <i>ab</i>-family of equations with cubic nonlinearities, which contains the integrable modified Camassa–Holm equation (<span>(a = frac{1}{3})</span>, <span>(b = 2)</span>) and the Novikov equation (<span>(a = 0)</span>, <span>(b = 3)</span>) as two special cases. When <span>(3a + b ne 3)</span>, the <i>ab</i>-family of equations does not possess the <span>(H^1)</span>-norm conservation law. We give the local well-posedness results of this Cauchy problem in Besov spaces and Sobolev spaces. Furthermore, we provide a blow-up criterion, the precise blow-up scenario and a sufficient condition on the initial data for the blow-up of strong solutions to the <i>ab</i>-family of equations. Our blow-up analysis does not rely on the use of the conservation laws.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139945824","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
Linear Instability of Symmetric Logarithmic Spiral Vortex Sheets 对称对数螺旋涡旋片的线性不稳定性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-23 DOI: 10.1007/s00021-023-00847-y
Tomasz Cieślak, Piotr Kokocki, Wojciech S. Ożański
{"title":"Linear Instability of Symmetric Logarithmic Spiral Vortex Sheets","authors":"Tomasz Cieślak,&nbsp;Piotr Kokocki,&nbsp;Wojciech S. Ożański","doi":"10.1007/s00021-023-00847-y","DOIUrl":"10.1007/s00021-023-00847-y","url":null,"abstract":"<div><p>We consider Alexander spirals with <span>(Mge 3)</span> branches, that is symmetric logarithmic spiral vortex sheets. We show that such vortex sheets are linearly unstable in the <span>(L^infty )</span> (Kelvin–Helmholtz) sense, as solutions to the Birkhoff–Rott equation. To this end we consider Fourier modes in a logarithmic variable to identify unstable solutions with polynomial growth in time.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139945823","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
Temporal Regularity of Symmetric Stochastic p-Stokes Systems 对称随机 p-Stokes 系统的时间规律性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-21 DOI: 10.1007/s00021-024-00852-9
Jörn Wichmann
{"title":"Temporal Regularity of Symmetric Stochastic p-Stokes Systems","authors":"Jörn Wichmann","doi":"10.1007/s00021-024-00852-9","DOIUrl":"10.1007/s00021-024-00852-9","url":null,"abstract":"<div><p>We study the symmetric stochastic <i>p</i>-Stokes system, <span>(p in (1,infty ))</span>, in a bounded domain. The results are two-fold: First, we show that in the context of analytically weak solutions, the stochastic pressure—related to non-divergence free stochastic forces—enjoys almost <span>(-1/2)</span> temporal derivatives on a Besov scale. Second, we verify that the velocity <i>u</i> of strong solutions obeys 1/2 temporal derivatives in an exponential Nikolskii space. Moreover, we prove that the non-linear symmetric gradient <span>(V(mathbb {epsilon } u) = (kappa + left| mathbb {epsilon } uright| )^{(p-2)/2} mathbb {epsilon } u)</span>, <span>(kappa ge 0)</span>, which measures the ellipticity of the <i>p</i>-Stokes system, has 1/2 temporal derivatives in a Nikolskii space.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00852-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139923822","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
Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction 流体-硬球相互作用随时间变化的运动稳定性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-19 DOI: 10.1007/s00021-024-00854-7
Toshiaki Hishida
{"title":"Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction","authors":"Toshiaki Hishida","doi":"10.1007/s00021-024-00854-7","DOIUrl":"10.1007/s00021-024-00854-7","url":null,"abstract":"<div><p>We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the incompressible Navier–Stokes system, whereas the motion of the body is governed by the balance for linear and angular momentum. Both motions are affected by each other at the boundary. Assuming that the rigid body is a ball, we adopt a monolithic approach to deduce <span>(L^q)</span>–<span>(L^r)</span> decay estimates of solutions to a non-autonomous linearized system. We then apply those estimates to the full nonlinear initial value problem to find temporal decay properties of the disturbance. Although the shape of the body is not allowed to be arbitrary, the present contribution is the first attempt at analysis of the large time behavior of solutions around nontrivial basic states, that can be time-dependent, for the fluid–structure interaction problem and provides us with a stability theorem which is indeed new even for steady motions under the self-propelling condition or with wake structure.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00854-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903174","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
On a Stokes System Arising in a Free Surface Viscous Flow of a Horizontally Periodic Fluid with Fractional Boundary Operators 关于水平周期流体自由表面粘性流动中出现的斯托克斯系统与分数边界算子
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-12 DOI: 10.1007/s00021-023-00850-3
Daisuke Hirata
{"title":"On a Stokes System Arising in a Free Surface Viscous Flow of a Horizontally Periodic Fluid with Fractional Boundary Operators","authors":"Daisuke Hirata","doi":"10.1007/s00021-023-00850-3","DOIUrl":"10.1007/s00021-023-00850-3","url":null,"abstract":"<div><p>In this note we investigate the initial-boundary value problem for a Stokes system arising in a free surface viscous flow of a horizontally periodic fluid with fractional boundary operators. We derive an integral representation of solutions by making use of the multiple Fourier series. Moreover, we demonstrate a unique solvability in the framework of the Sobolev space of <span>(L^2)</span>-type.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139750824","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
2D Voigt Boussinesq Equations 二维 Voigt 布森斯方程
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-02 DOI: 10.1007/s00021-023-00849-w
Mihaela Ignatova
{"title":"2D Voigt Boussinesq Equations","authors":"Mihaela Ignatova","doi":"10.1007/s00021-023-00849-w","DOIUrl":"10.1007/s00021-023-00849-w","url":null,"abstract":"<div><p>We consider a critical conservative Voigt regularization of the 2D incompressible Boussinesq system on the torus. We prove the existence and uniqueness of global smooth solutions and their convergence in the smooth regime to the Boussinesq solution when the regularizations are removed. We also consider a range of mixed (subcritical–supercritical) Voigt regularizations for which we prove the existence of global smooth solutions.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139670224","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
Diffusion Enhancement and Taylor Dispersion for Rotationally Symmetric Flows in Discs and Pipes 圆盘和管道中旋转对称流动的扩散增强和泰勒扩散
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-01-27 DOI: 10.1007/s00021-023-00845-0
Michele Coti Zelati, Michele Dolce, Chia-Chun Lo
{"title":"Diffusion Enhancement and Taylor Dispersion for Rotationally Symmetric Flows in Discs and Pipes","authors":"Michele Coti Zelati,&nbsp;Michele Dolce,&nbsp;Chia-Chun Lo","doi":"10.1007/s00021-023-00845-0","DOIUrl":"10.1007/s00021-023-00845-0","url":null,"abstract":"<div><p>In this note, we study the long-time dynamics of passive scalars driven by rotationally symmetric flows. We focus on identifying precise conditions on the velocity field in order to prove enhanced dissipation and Taylor dispersion in three-dimensional infinite pipes. As a byproduct of our analysis, we obtain an enhanced decay for circular flows on a disc of arbitrary radius.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00845-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139582751","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
From Bipolar Euler-Poisson System to Unipolar Euler-Poisson One in the Perspective of Mass 质量视角下从双极欧拉-泊松系统到单极欧拉-泊松系统
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-01-16 DOI: 10.1007/s00021-023-00838-z
Shuai Xi, Liang Zhao
{"title":"From Bipolar Euler-Poisson System to Unipolar Euler-Poisson One in the Perspective of Mass","authors":"Shuai Xi,&nbsp;Liang Zhao","doi":"10.1007/s00021-023-00838-z","DOIUrl":"10.1007/s00021-023-00838-z","url":null,"abstract":"<div><p>The main purpose of this paper is to provide an effective procedure to study rigorously the relationship between unipolar and bipolar Euler-Poisson systems in the perspective of mass. Based on the fact that the mass of an electron is far less than that of an ion, we amplify this property by letting <span>(m_e/m_irightarrow 0)</span> and using two different singular limits to illustrate it, which are the zero-electron mass limit and the infinity-ion mass limit. We use the method of asymptotic expansions to handle the problem and find that the limiting process from bipolar to unipolar systems is actually the process of decoupling, but not the vanishing of equations of the corresponding the other particle.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139475377","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
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