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

Seria
Rozprawy Matematyczne tom/nr w serii: 304 wydano: 1990-01-23
Zawartość
Warianty tytułu
Abstrakty
EN

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.
EN

CONTENTS
1. Introduction................................................................5
2. Problem (1-1) in a half-space.....................................7
3. A priori estimate and existence of solutions of problem (1.1) with vanishing initial conditions............................20
4. Existence of solutions of problem (1.1)....................28
References..................................................................33
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 304
Liczba stron
33
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCIV
Daty
wydano
1990-01-23
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-950 Warsaw, Poland
Bibliografia
  • [1] V. A. Solonnikov, On an initial-boundary value problem for the Stokes system which appears in problems with free boundary (to appear) (in Russian).
  • [2] V. A. Solonnikov, On boundary problems for linear parabolic systems of differential equations of general form, Trudy Mat. Inst. Steklov. 83 (1965) (in Russian).
  • [3] W. M. Zajączkowski, On nonstationary motion of a compressible barotropic viscous capillary fluid bounded by a free surface, SIAM J. Math. Anal, (submitted).
  • [4] W. M. Zajączkowski and B. Zawisza, On global nonstationary motion of a general compressible viscous capillary fluid bounded by a free surface(to appear).
Języki publikacji
EN
Uwagi
1985 Mathematics Subject Classification: 35K15, 35K20, 35Q10.
Identyfikator YADDA
bwmeta1.element.zamlynska-84acd7ec-ec2f-4c08-ae93-ba656e658617
Identyfikatory
ISBN
83-85116-03-6
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

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