Global solutions to compressible Navier-Stokes-Poisson and Euler-Poisson equations of plasma on exterior domains

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

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Detail(s)

Original languageEnglish
Pages (from-to)9936-10001
Journal / PublicationJournal of Differential Equations
Volume269
Issue number11
Online published13 Jul 2020
Publication statusPublished - 15 Nov 2020

Abstract

The initial boundary value problems for compressible Navier-Stokes-Poisson and Euler-Poisson equations of plasma are considered on exterior domains in this paper. With the radial symmetry assumption, the global existence of solutions to compressible Navier-Stokes-Poisson equations with the large initial data on a domain exterior to a ball in ℝn(n ≥ 1) is proved. Moreover, without any symmetry assumption, the global existence of smooth solutions near a given constant steady state for both compressible Navier-Stokes-Poisson and Euler-Poisson equations on an exterior domain in ℝ3 with physical boundary conditions is also established with the exponential stability. A key issue addressed in this paper is on the global-in-time regularity of solutions near physical boundaries. This is in particular so for the 3-D compressible Navier-Stokes-Poisson equations to which global smooth solutions of initial boundary value problems are seldom found in literature to the best of knowledge.

Research Area(s)

  • Exponential stability, Exterior domain, Global regularity near boundaries