Vanishing viscosity of isentropic Navier-Stokes equations for interacting shocks  

作　　者：HUANG FeiMin WANG Yi WANG Yong YANG Tong 

机构地区：[1]Institute of Applied Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences [2]Department of Mathematics, City University of Hong Kong

出　　处：《Science China Mathematics》2015年第4期653-672,共20页中国科学：数学（英文版）

基　　金：supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002);the National Center for Mathematics and Interdisciplinary Sciences,Academy of Mathematics and Systems Science,Chinese Academy of Sciences and the Chinese Academy of Sciences Program for Cross&Cooperative Team of the Science&Technology Innovation,National Natural Sciences Foundation of China(Grant Nos.11171326,11371064 and 11401565);the General Research Fund of Hong Kong(Grant No.City U 103412)

摘　　要：We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to p-system which consists of two different families of shocks interacting at some positive time,we show that such entropy solution is the vanishing viscosity limit of a family of global smooth solutions to the isentropic Navier-Stokes equations. The key point of the proofs is to derive the estimates separately before and after the interaction time and connect the incoming and outgoing viscous shock profiles.We study the vanishing viscosity of the Navier-Stokes equations for interacting shocks. Given an entropy solution to p-system which consists of two different families of shocks interacting at some positive time,we show that such entropy solution is the vanishing viscosity limit of a family of global smooth solutions to the isentropic Navier-Stokes equations. The key point of the proofs is to derive the estimates separately before and after the interaction time and connect the incoming and outgoing viscous shock profiles.

关 键 词：isentropic Navier-Stokes equations isentropic Euler equations interacting shock vanishing viscosity entropy solution 

分 类 号：O175[理学—数学]