Year: 2024
Author: Beixiang Fang, Ya-Guang Wang
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 3 : pp. 402–424
Abstract
In this paper we show that, as the viscosity is properly small, there exists a viscous transonic shock solution for the steady 1-D Navier-Stokes system with prescribed pressure at the exit, and it converges to a transonic shock solution to the 1-D steady Euler system as the viscosity goes to zero. Moreover, the position of the shock front is also derived. The key step is to reduce the pressure condition at the exit into a nonlinear boundary condition on the velocity, such that the boundary value problem for the Navier-Stokes system can be reformulated as a boundary value problem for an ODE with an unknown parameter.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2024-0017
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 3 : pp. 402–424
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Asymptotic analysis steady 1-D viscous shocks 1-D finite nozzle small viscous limits Euler system Navier-Stokes system.