Global weak solutions to 3D compressible Navier-Stokes-Poisson equations with density-dependent viscosity

TL;DR

This paper proves the existence of global weak solutions for the 3D compressible Navier-Stokes-Poisson equations with density-dependent viscosity and damping, using advanced mathematical techniques under specific conditions on the adiabatic constant.

Contribution

It establishes the existence of global weak solutions for a complex fluid dynamics system with density-dependent viscosity and non-monotone pressure, extending previous theoretical results.

Findings

Existence of global weak solutions for a4a4a4a4a4a4a4a4 equations with damping.

Solutions exist for large initial data in a three-dimensional torus.

The proof employs Faedo-Galerkin and compactness methods under b3 > 4/3.

Abstract

Global-in-time weak solutions to the Compressible Navier-Stokes-Poisson equations in a three-dimensional torus for large data are considered in this paper. The system takes into account density-dependent viscosity and non-monotone presseur. We prove the existence of global weak solutions to NSP equations with damping term by using the Faedo-Galerkin method and the compactness arguments on the condition that the adiabatic constant satisfies $\gamma>\frac{4}{3}$.