# On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations

- Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1990

## Access Full Book

top## Abstract

top## How to cite

topW. M. Zajączkowski. On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1990. <http://eudml.org/doc/268448>.

@book{W1990,

abstract = {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..................................................................331985 Mathematics Subject Classification: 35K15, 35K20, 35Q10.},

author = {W. M. Zajączkowski},

keywords = {Sobolev-Slobodetskij spaces; existence; uniqueness},

language = {eng},

location = {Warszawa},

publisher = {Instytut Matematyczny Polskiej Akademi Nauk},

title = {On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations},

url = {http://eudml.org/doc/268448},

year = {1990},

}

TY - BOOK

AU - W. M. Zajączkowski

TI - On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations

PY - 1990

CY - Warszawa

PB - Instytut Matematyczny Polskiej Akademi Nauk

AB - 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..................................................................331985 Mathematics Subject Classification: 35K15, 35K20, 35Q10.

LA - eng

KW - Sobolev-Slobodetskij spaces; existence; uniqueness

UR - http://eudml.org/doc/268448

ER -

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.