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.
"Time-periodic approximations of the Euler–Poisson system near Lane–Emden stars." Anal. PDE 9 (5) 1043 - 1078, 2016. https://doi.org/10.2140/apde.2016.9.1043