On $$L^2$$ decay of weak solutions of several incompressible fluid models

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-06-22 DOI:10.1007/s00028-024-00985-4

Huan Yu

引用次数: 0

Abstract

In this paper, we are concerned with $L^2$ decay of weak solutions of several well-known incompressible fluid models, such as the n-dimensional ($n\ge 2$) Navier–Stokes equations with fractional hyperviscosity, the three-dimensional convective Brinkman–Forchheimer equations and the generalized SQG equation. A new approach, different from the classical Fourier splitting method develpoed by Schonbek (Commun Partial Differ Equ 11:733–763, 1986) and the spectral representation technique by Kajikiya and Miyakawa (Math Z 192:135-148,1986), is presented. By using the new approach, we can recover and improve some known decay results.

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论若干不可压缩流体模型弱解的 $$L^2$$ 衰减

在本文中，我们关注几种著名不可压缩流体模型弱解的（L^2）衰减，如 n 维（n\ge 2\)纳维-斯托克斯方程（Navier-Stokes equations with fractional hyperviscosity）、三维对流布林克曼-福克海默方程（the three-dimensional convective Brinkman-Forchheimer equations）和广义 SQG 方程。与 Schonbek（Commun Partial Differ Equ 11:733-763, 1986）提出的经典傅立叶分裂法以及 Kajikiya 和 Miyakawa（Math Z 192:135-148,1986）提出的谱表示技术不同，本文提出了一种新方法。通过使用新方法，我们可以恢复和改进一些已知的衰变结果。

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