一维可压Navier-Stokes方程全局弱解的渐近性态

摘要

研究一维情形下可压Navier-Stokes方程的自由边值问题.假设初始密度间断连续到真空.先通过建立一些先验估计式得到密度ρ的正上下界,再利用磨光初值法构造光滑逼近解.当粘性系数μ(ρ)=1+θρ0,θ＞0时,证明了弱解的全局存在性,进而讨论了全局弱解的渐近性态.%One-dimensional compressible Navier-Stokes equations with free boundary value problem is studied. The initial density is assumed to be connected to vacuum discontinuously. The positive upper and lower bound of the density p is obtained by using some priori estimates, and then smooth approximate solutions are constructed by defining the approximate initial data. The existence of global weak solutions is proved when the viscosity coefficient μ(ρ) = 1 + θρθ, θ>0. Moreover, asymptotic behavior of global weak solutions is discussed.