The existence and uniqueness of solutions of an initial-boundary value problem for the second order linear parabolic system which appears in free boundary problems for compressible Navier-Stokes equations are proved. Moreover, an estimate in anisotropic Sobolev-Slobodetskii spaces with noninteger derivatives is found. The existence and regularity of solutions are shown by means of a regularizer in the same way as in the case of general parabolic systems. However, the problem must be considered separately because the boundary conditions are noncoercive. Moreover, Sobolev-Slobodetskii spaces with noninteger derivatives are used' because both first and second order operators appear in the boundary conditions.
CONTENTS1. Introduction................................................................52. Problem (1-1) in a half-space.....................................73. A priori estimate and existence of solutions of problem (1.1) with vanishing initial conditions............................204. Existence of solutions of problem (1.1)....................28References..................................................................33
1985 Mathematics Subject Classification: 35K15, 35K20, 35Q10.
@book{bwmeta1.element.zamlynska-84acd7ec-ec2f-4c08-ae93-ba656e658617,
author = {W. M. Zaj\k aczkowski},
title = {On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1990},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-84acd7ec-ec2f-4c08-ae93-ba656e658617}
}
W. M. Zajączkowski. On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations. GDML_Books (1990), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-84acd7ec-ec2f-4c08-ae93-ba656e658617/