Global Solution of Euler-Poisson System in the Inviscid Limit of Navier-Stokes-Poisson System with General Density Dependent Viscosities

Abstract

Based on delicate construction of approximate initial data sequence, elaborate estimates on the viscous terms and elegant analysis of the convergence of momentum equation, we succeed in establishing the global existence of spherically symmetric finite-energy weak solution of the compressible Euler-Poisson equations for large initial data through justifying the inviscid limit of the solutions of Navier-Stokes-Poisson equations with a very general class of density-dependent viscosities. Our results can serve as an extension of [Chen et al., Comm. Pure Appl. Math. 77(6) (2024)].