可压Navier-Stokes方程解的最高阶导的最佳衰减估计

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 345-356.

可压Navier-Stokes方程解的最高阶导的最佳衰减估计

陈卿()

^{厦门理工学院应用数学学院福建厦门 361024}

收稿日期:2020-03-23 出版日期:2021-04-26 发布日期:2021-04-29
作者简介:陈卿, E-mail: chenqing@xmut.edu.cn
基金资助:
福建省自然科学基金(2018J01430)

Optimal Time Decay Rate of the Highest Derivative of Solutions to the Compressible Navier-Stokes Equations

Qing Chen()

^{School of Applied Mathematics, Xiamen University of Technology, Fujian Xiamen 361024}

Received:2020-03-23 Online:2021-04-26 Published:2021-04-29
Supported by:
the NSF of Fujian Province(2018J01430)

摘要/Abstract

摘要：

该文研究可压Navier-Stokes方程Cauchy问题光滑解的衰减估计问题.假设初始扰动在 $H^l(\mathbb{R}^3)(l\geq3)$ 中充分小，且属于 $\dot{H}^{-s}(\mathbb{R}^3)(0\le s < \frac52)$ ，通过对解的高低频分解，结合谱分析和能量估计方法，得到解各阶导数的最佳衰减估计结果.

关键词: 可压流, 最佳衰减, 能量方法

Abstract:

In this paper, we are concerned with the time decay rates of smooth solutions to the Cauchy problem for the compressible Navier-Stokes equations. Under the assumptions that the initial data are close to the constant equilibrium state in $H^l(\mathbb{R}^3)$ with $l\geq3$ and belong to $\dot{H}^{-s}(\mathbb{R}^3)$ with $0 \le s < \frac52$ , via decomposing the solutions into the low- and high-frequency parts, we establish the optimal convergence rates of all the derivatives of the solution by combining spectral analysis and the energy method.

Key words: Compressible flow, Optimal decay, Energy method

中图分类号:

O175.2

陈卿. 可压Navier-Stokes方程解的最高阶导的最佳衰减估计[J]. 数学物理学报, 2021, 41(2): 345-356.

Qing Chen. Optimal Time Decay Rate of the Highest Derivative of Solutions to the Compressible Navier-Stokes Equations[J]. Acta mathematica scientia,Series A, 2021, 41(2): 345-356.

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