Global solutions to physical vacuum problem of non-isentropic viscous gaseous stars and nonlinear asymptotic stability of stationary solutions

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

4 Scopus Citations
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Original languageEnglish
Pages (from-to)177-236
Journal / PublicationJournal of Differential Equations
Volume265
Issue number1
Online published7 Mar 2018
Publication statusPublished - 5 Jul 2018

Abstract

This paper is concerned with spherically symmetric motions of non-isentropic viscous gaseous stars with self-gravitation. When the stationary entropy S‾(x) is spherically symmetric and satisfies a suitable smallness condition, the existence and properties of the stationary solutions are obtained for 6/5<γ<2 with weaker constraints upon S‾(x) compared with the one in [26], where γ is the adiabatic exponent. The global existence of strong solutions capturing the physical vacuum singularity that the sound speed is C½-Hölder continuous across the vacuum boundary to a simplified system for non-isentropic viscous flow with self-gravitation and the nonlinear asymptotic stability of the stationary solution are proved when 4/3<γ<2 with the detailed convergence rates, motivated by the results and analysis of the nonlinear asymptotic stability of Lane–Emden solutions for isentropic flows in [29,30].

Research Area(s)

  • Navier–Stokes–Poisson equations, Non-isentropic flow, Nonlinear asymptotic stability, Physical vacuum

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