可压Navier-Stokes方程解的最高阶导的最佳衰减估计  

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

作　　者：陈卿 Chen Qing(School of Applied Mathematics,Xiamen University of Technology,Fujian Xiamen 361024)

机构地区：[1]厦门理工学院应用数学学院,福建厦门361024

出　　处：《数学物理学报（A辑）》2021年第2期345-356,共12页Acta Mathematica Scientia

基　　金：福建省自然科学基金(2018J01430)。

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)(R^(3))(l≥3)中充分小,且属于H^(-s)(R^(3))(0≤s<5/2),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.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)(R^(3))with l≥3 and belong to H^(˙)^(−s)(R3)with 0≤s<52,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.

关 键 词：可压流 最佳衰减 能量方法 

分 类 号：O175.2[理学—数学]