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

W. 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 -