2010/04/01 by Quansen Jiu, Yi Wang, Jiu, Quansen +3
Engineering · Mathematics · #35L60 #35L65 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #math.AP #msc:35L60 #msc:35L65
paper · pdf · doi:10.48550/arxiv.1004.0036
30 pages
arxiv created 2010/04/01 · openalex publication_date 2010/04/01 · arxiv updated 2010/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is constructed by approximating the system and regularizing the initial values which may contain vacuum state. Then some global in time estimates on the weak solution are obtained. Based on these uniform estimates, the vacuum states are shown to vanish in finite time and the weak solution we constructed becomes a unique strong one. Consequently, the stability of the rarefaction wave is proved in a weak sense. The theory holds for large-amplitudes rarefaction waves and arbitrary initial perturbations.