Vanishing viscosity of isentropic Navier-Stokes equations for interacting shocks

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...

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Bibliographic Details
Published in:Science China. Mathematics 2015-04, Vol.58 (4), p.653-672
Main Authors: Huang, FeiMin, Wang, Yi, Wang, Yong, Yang, Tong
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
Navier-Stokes方程
p系统
家庭
次冲击
相互作用时间
等熵
粘度
粘性激波
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Summary: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.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-014-4962-4