Vol. 9, No. 5, 2016
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Time-periodic approximations of the Euler–Poisson system near Lane–Emden stars

Juhi Jang
Vol. 9 (2016), No. 5, 1043–1078
DOI: 10.2140/apde.2016.9.1043
Abstract

We show a long-time validity of the time-periodic linear approximations to the gravitational Euler–Poisson system near Lane–Emden equilibria for all relevant adiabatic exponents. To prove the result, we reformulate the problem in Lagrangian coordinates and use the weighted energy estimates together with Hardy inequalities.

Keywords
Euler–Poisson system, Lane–Emden solutions, physical vacuum boundary, time-periodic approximation
Mathematical Subject Classification 2010
Primary: 35L80, 35Q05, 35R37
Milestones
Received: 18 September 2015
Revised: 17 February 2016
Accepted: 30 March 2016
Published: 29 July 2016
Authors
Juhi Jang
Department of Mathematics
University of Southern California
Los Angeles, CA 90089
United States