Mathematical analysis of the motion of a piston in a fluid with density dependent viscosity

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-09-07 DOI:10.1007/s00028-024-01006-0

Vaibhav Kumar Jena, Debayan Maity, Abu Sufian

引用次数: 0

Abstract

We study a free boundary value problem modelling the motion of a piston in a viscous compressible fluid. The fluid is modelled by 1D compressible Navier–Stokes equations with possibly degenerate viscosity coefficient, and the motion of the piston is described by Newton’s second law. We show that the initial boundary value problem has a unique global in time solution, and we also determine the large time behaviour of the system. Finally, we show how our methodology may be adapted to the motion of several pistons.

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活塞在粘性随密度变化的流体中运动的数学分析

我们研究了一个模拟活塞在粘性可压缩流体中运动的自由边界值问题。流体由一维可压缩纳维-斯托克斯方程建模，该方程可能具有退化粘度系数，活塞的运动由牛顿第二定律描述。我们证明了初始边界值问题具有唯一的全局时间解，我们还确定了系统的大时间行为。最后，我们展示了我们的方法如何适用于多个活塞的运动。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators