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 sho...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.展开更多
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)
文摘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.
