Open AccessUniqueness of steady 1-D shock solutions in a finite nozzle via vanishing viscosity aguments
Author(s) -
Beixiang Fang,
Qin Zhao
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021066
Subject(s) - uniqueness , inviscid flow , shock (circulatory) , physics , viscosity , barotropic fluid , mathematics , mathematical analysis , shock front , thermodynamics , shock wave , mechanics , medicine
This paper studies the uniqueness of steady 1-D shock solutions in a finite flat nozzle via vanishing viscosity arguments. It is proved that, for both barotropic gases and non-isentropic gases, the steady viscous shock solutions converge under the \begin{document}$ \mathcal{L}^{1} $\end{document} norm. Hence only one shock solution of the inviscid Euler system could be the limit as the viscosity coefficient goes to \begin{document}$ 0 $\end{document} , which shows the uniqueness of the steady 1-D shock solution in a finite flat nozzle. Moreover, the position of the shock front for the limit shock solution is also obtained.