TY - JOUR
T1 - Asymptotic Analysis of Steady Viscous Shocks in a 1-D Finite Nozzle in the Small Viscosity Limit
AU - Fang , Beixiang
AU - Wang , Ya-Guang
JO - Communications in Mathematical Analysis and Applications
VL - 3
SP - 402
EP - 424
PY - 2024
DA - 2024/09
SN - 3
DO - http://doi.org/10.4208/cmaa.2024-0017
UR - https://global-sci.org/intro/article_detail/cmaa/23382.html
KW - Asymptotic analysis, steady 1-D viscous shocks, 1-D finite nozzle, small
viscous limits, Euler system, Navier-Stokes system.
AB - <p style="text-align: justify;">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.</p>