带外力的可压缩Navier-Stokes方程的自由边界问题

摘要

研究黏性系数μ(ρ)=ρα,α∈(0,1]的一维等熵可压缩Navier-Stokes方程的自由边界问题,通过对一维等熵可压缩Navier-Stokes方程的能量估计、新熵估计、密度上下界等先验估计和对于非真空的正则初始值,可以把一维等熵可压缩Navier-Stokes方程的抛物方程按线性热方程来考虑,则证明该问题存在唯一的整体强解。%This paper is about the free boundary value problem to one-dimensional isentropic compressible Navier-Stokes equations with stress free boundary condition and density-dependent viscosityμ(ρ) =ρα,α∈(0,1]. It is proved that there is a unique global strong solution to the problem when the one dimensional isentropic compressi-ble Navier-Stokes equations are considered as a linear system through energy estimate, a new entropy estimate, and upper and lower bounds of the density estimate, etc.