Instability theory of the Navier–Stokes–Poisson equations

Jang, Juhi; Tice, Ian

doi:10.2140/apde.2013.6.1121

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Instability theory of the Navier–Stokes–Poisson equations

Juhi Jang and Ian Tice

Vol. 6 (2013), No. 5, 1121–1181

DOI: 10.2140/apde.2013.6.1121

Abstract

The stability question of the Lane–Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane–Emden solutions in the framework of the Navier–Stokes–Poisson system with adiabatic exponent $\frac{6}{5} < γ < \frac{4}{3}$ .

Keywords

Navier–Stokes–Poisson, free boundary problems, gaseous stars, hydrodynamic instability, nonlinear instability

Mathematical Subject Classification 2010

Primary: 35Q30, 35R35, 76E20, 85A30

Milestones

Received: 5 July 2012

Revised: 4 January 2013

Accepted: 28 February 2013

Published: 3 November 2013

Authors

Juhi Jang
Department of Mathematics University of California, Riverside Riverside, CA 92521 United States

Ian Tice
Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213 United States

Vol. 6, No. 5, 2013