2025/02/12 by Sung-Ho Han, Moon-Jin Kang, Han, Sungho +7 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Differential Equations and Numerical Methods #FOS: Mathematics #Gas Dynamics and Kinetic Theory
paper · pdf · doi:10.48550/arxiv.2502.08126
openalex publication_date 2025/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
We establish the asymptotic stability of solutions to the inflow problem for the one-dimensional barotropic Navier--Stokes equations in half space. When the boundary value is located at the subsonic regime, all the possible thirteen asymptotic patterns are classified in \citeM01. We consider the most complicated pattern, the superposition of the boundary layer solution, the 1-rarefaction wave, and the viscous 2-shock waves. In this superposition, the boundary layer is degenerate and large. We prove that, if the strengths of the rarefaction wave and shock wave are small, and if the initial data is a small perturbation of the superposition, then the solution asymptotically converges to the superposition up to a dynamical shift for the shock. As a corollary, our result implies the asymptotic stability for the simpler case where the superposition consists of the degenerate boundary layer solution and the viscous 2-shock. Therefore, we complete the study of the asymptotic stability of the inflow problem for the 1D barotropic Navier--Stokes equations for subsonic boundary values.