一维可压Navier-Stokes方程全局弱解的渐近性态  

Asymptotic behavior of global weak solutions to 1D compressible Navier-Stokes equations

作　　者：宋红丽[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《纺织高校基础科学学报》2012年第3期292-298,共7页Basic Sciences Journal of Textile Universities

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+θρθ,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 ρ 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,θ0.Moreover,asymptotic behavior of global weak solutions is discussed.

关 键 词：NAVIER-STOKES方程 自由边值 存在性 渐近性态 

分 类 号：O175.2[理学—数学]