We consider the motion of a viscous compressible barotropic fluid in bounded by a free surface which is under constant exterior pressure. For a given initial density, initial domain and initial velocity we prove the existence of local-in-time highly regular solutions. Next assuming that the initial density is sufficiently close to a constant, the initial pressure is sufficiently close to the external pressure, the initial velocity is sufficiently small and the external force vanishes we prove the existence of global-in-time solutions which satisfy, at any moment of time, the properties prescribed at the initial moment.
1991 Mathematics Subject Classification: 35A05, 35R35, 76N10.
CONTENTS1. Introduction.......................................52. Global estimates and relations........113. Local existence...............................164. Global differential inequality............445. Korn inequality................................816. Global existence.............................89References.......................................100
@book{bwmeta1.element.zamlynska-a47e081b-3af2-4f6b-bdd3-d756024211c4,
author = {Wojciech M. Zaj\k aczkowski},
title = {On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1993},
zbl = {0771.76059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-a47e081b-3af2-4f6b-bdd3-d756024211c4}
}
Wojciech M. Zajączkowski. On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface. GDML_Books (1993), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-a47e081b-3af2-4f6b-bdd3-d756024211c4/