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## On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface

Autorzy
Seria
Rozprawy Matematyczne tom/nr w serii: 324 wydano: 1993
Zawartość
Warianty tytułu
Abstrakty
EN
We consider the motion of a viscous compressible barotropic fluid in $ℝ^3$ 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.

CONTENTS
1. Introduction.......................................5
2. Global estimates and relations........11
3. Local existence...............................16
4. Global differential inequality............44
5. Korn inequality................................81
6. Global existence.............................89
References.......................................100
Słowa kluczowe
Tematy
Kategoryzacja MSC:
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 324
Liczba stron
101
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXXIV
Daty
wydano
1993
otrzymano
1991-07-03
poprawiono
1992-01-28
poprawiono
1992-08-31
Twórcy
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland
Bibliografia
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• [35] W. M. Zajączkowski, On nonstationary motion of a compressible viscous capillary fluid bounded by a free surface, to appear.
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• [37] W. M. Zajączkowski, Local existence of solutions for free boundary problems for viscous fluids, to appear.
Języki publikacji
 EN
Uwagi
1991 Mathematics Subject Classification: 35A05, 35R35, 76N10.
Identyfikator YADDA
bwmeta1.element.zamlynska-a47e081b-3af2-4f6b-bdd3-d756024211c4
Identyfikatory
ISBN
83-85116-81-8
ISSN
0012-3862
Kolekcja
DML-PL
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