Regularity of weak solution of the compressible Navier-Stokes equations with self-consistent Poisson equation by Moser iteration

Abstract

<abstract><p>In this paper, we consider the regularity of the weak solution to the compressible Navier-Stokes-Poisson equations in period domain $ \Omega \subseteq \mathbb{R}^3 $ provided that the density $ \rho(t, x) $ with integrability on the space $ L^{\infty}(0, T;L^{q_0}(\Omega)) $ where $ q_0 $ satisfies a certain condition and $ T > 0 $, by which we could present that $ \sup_{t, x}\rho(t, x) < \infty $ and $ \inf_{t, x}\rho(t, x) > 0 $. Furthermore, we develop the estimate for the velocity $ \Vert u\Vert_{L^{\infty}} $ by the Moser iteration method and Gronwall inequality.</p></abstract>