## Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow

### Volume 185 / 2008

Studia Mathematica 185 (2008), 99-125
MSC: 35Q30, 47D06, 76E20.
DOI: 10.4064/sm185-2-1

#### Abstract

We prove *a priori* estimates for a linear system of partial differential equations originating from the equations for the flow of a barotropic compressible viscous fluid under the influence of the gravity it generates. These estimates will be used in a forthcoming paper to prove the nonlinear stability of the motionless, spherically symmetric equilibrium states of barotropic, self-gravitating viscous fluids with respect to perturbations of zero total angular momentum. These equilibrium states as well as the non-stationary solutions occupy part of space, and a constant pressure is assumed on the free surface, but no surface tension.