The Solvability to the Compressible Isentropic Navier-Stokes Equations

Abstract

众所周知,现实世界中许许多多的流体运动规律都可以用可压等熵~Navier-Stokes~方程来刻画．因此,对这类可压流体方程的研究不仅有理论意义,而且有重要的实际应用价值．本文主要研究粘性系数依赖密度的含真空的三维可压等熵~Navier-Stokes~方程的局部古典解存在性与一般初值常粘性系数的三维含真空可压等熵~Navier-Stokes~方程的整体光滑解存在性． 本文在第二章证明了粘性系数依赖于密度(~$\mu(\rho),\\lambda(\rho)$~)、三维含真空可压等熵~Navier-Stokes~方程的局部古典解存在性．克服的主要困难是其中线性化技巧和非线性椭圆方程理论的应...It's well known that the Navier-Stokes equations is the model describing the motion of fluids. The research of compressible fluids has the important theory significance and strong application value. This article is mainly concerned with the local existence of classical solutions with density-dependent viscosity coefficients, and the global existence of classical solutions with general initial dat...学位：理学博士院系专业：数学科学学院_基础数学学号：1902010015395