2009/12/24 by Shuichi Kawashima, Tohru Nakamura, Kawashima, Shuichi +5 · 1 citation
Engineering · Mathematics · #35B35 #35B40 #76N15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Dynamical Systems (math.DS) #FOS: Mathematics #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.0912.4839
openalex publication_date 2009/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper is concerned with large-time behavior of solutions to an outflow problem for an ideal polytropic model of compressible viscous gases in one-dimensional half space, and with a convergence rate of solutions toward a corresponding stationary solution. With the aid of center manifold theory, we prove the existence of the stationary solution, under a smallness condition on the boundary data. We also investigate, by employing an energy method, the time asymptotic stability of the stationary solution under suitable smallness assumptions, and estimate the convergence rate which coincides with the spatial decay rate of the initial perturbation. The proof is mainly based on a priori estimates, which are derived by a time and space weighted energy method.