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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-2-1,
author = {Gerhard Str\"ohmer},
title = {Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {99-125},
zbl = {1165.35042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-2-1}
}
Gerhard Ströhmer. Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow. Studia Mathematica, Tome 187 (2008) pp. 99-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm185-2-1/