具有动态边界条件的二维 NSE 的强解和吸引子维度

IF 1.1 3区数学 Q1 MATHEMATICS Journal of Evolution Equations Pub Date : 2024-03-15 DOI:10.1007/s00028-024-00948-9

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引用次数: 0

摘要

摘要我们考虑了有界二维域中的不可压缩纳维-斯托克斯方程，其中包含所谓的动态滑移边界条件。假设数据是规则的，我们证明弱解是强解。作为一种应用，我们根据物理参数提供了全局吸引子分形维度的明确上限。这些估计值与 Dirichlet 边界条件情况下的类似结果一致。

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Strong solutions and attractor dimension for 2D NSE with dynamic boundary conditions

Abstract

We consider incompressible Navier–Stokes equations in a bounded 2D domain, complete with the so-called dynamic slip boundary conditions. Assuming that the data are regular, we show that weak solutions are strong. As an application, we provide an explicit upper bound of the fractal dimension of the global attractor in terms of the physical parameters. These estimates comply with analogous results in the case of Dirichlet boundary condition.

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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