Asymptotic Analysis of Steady Viscous Shocks in a 1-D Finite Nozzle in the Small Viscosity Limit

Asymptotic Analysis of Steady Viscous Shocks in a 1-D Finite Nozzle in the Small Viscosity Limit

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.

Author Details

Beixiang Fang

Ya-Guang Wang