一维可压Navier-Stokes方程自由边值问题全局强解存在性和解的边界行为  

Existence of Global Strong Solutions and Interface Behavior of Solutions for 1D Compressible Navier-Stokes Equations with Free Boundary Value Problem

作　　者：宋红丽[1] 郭真华[1] 

机构地区：[1]西北大学数学系,西北大学非线性科学研究中心,西安710127

出　　处：《数学物理学报（A辑）》2013年第4期601-620,共20页Acta Mathematica Scientia

基　　金：国家自然科学基金(11071195)资助

摘　　要：研究粘性系数μ(ρ)=1+θρθ时一维可压Navier-Stokes方程的自由边值问题.假设初始密度间断连续到真空.首先通过建立一些先验估计式得到了密度ρ的正上下界,其次利用磨光法构造光滑逼近解,证明了当θ＞0时全局弱解的存在唯一性,并且得到了解的边界行为及其渐近性态.进一步,在适当的初值条件下通过提高解的正则性证明了强解的全局存在性.In this paper,the authors study the free boundary problem for one-dimensional compressible Navier-Stokes equations when the viscosity coefficient μ(p) = 1 + θp~θ.The initial density is assumed to be connected to vacuum discontinuously.Firstly,the positive upper and lower bound of the density p is obtained by using some a priori estimates,and then the smooth approximate solutions are constructed by defining the approximate initial data.Finally,the authors prove the existence and uniqueness of global weak solutions when θ> 0 and the interface behavior,the asymptotic behavior of solutions are also obtained.Moreover,the regularity of global solution is established under appropriate assumptions imposed on the initial data,and then the existence of global strong solutions is proved.

关 键 词：NAVIER-STOKES方程 自由边值 强解 边界行为 渐近性态 

分 类 号：O175.2[理学—数学]