Communications in Mathematical Sciences
Volume 18 (2020)
Nonlinear stability of the boundary layer and rarefaction wave for the inflow problem governed by the heat-conductive ideal gas without viscosity
Pages: 2235 – 2261
This paper is devoted to studying the inflow problem for an ideal polytropic model with non-viscous gas in one-dimensional half space. We show the existence of the boundary layer in different areas. By employing the energy method, we also prove the unique global-in-time existence of the solution and the asymptotic stability of both the boundary layers, the $3$‑rarefaction wave and their superposition wave under some smallness conditions. Series of simple but tricky operations on boundary need to be carefully done by taking good advantage of construction on the system and domain properties.
non-viscous, inflow problem, boundary layer, rarefaction wave
2010 Mathematics Subject Classification
35B35, 35B40, 35M33, 35Q35, 76N10, 76N15
This work was supported by the Fundamental Research grants from the Science Foundation of Hubei Province under the contract 2018CFB693. The research of L.L. Fan was supported by the Natural Science Foundation of China #11871388 and and in part by the Natural Science Foundation of China #11701439.
Received 8 March 2020
Accepted 17 June 2020
Published 22 December 2020