2010/03/16 by Toan Nguyen, Toan T. Nguyen, Nguyen, Toan
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #math.AP
paper · pdf · doi:10.48550/arxiv.1003.3130
36 pages; this is a final revision, accepted for publication in JDE
openalex publication_date 2010/03/16 · arxiv created 2011/08/16 · arxiv updated 2011/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study nonlinear time-asymptotic stability of small--amplitude planar Lax shocks in a model consisting of a system of multi--dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is based on the earlier developments by Zumbrun for multi-dimensional viscous shock waves and by Lattanzio-Mascia-Nguyen-Plaza-Zumbrun for one--dimensional radiative shock profiles.