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

Wojciech M. Zajączkowski

  • Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1993

Abstract

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We consider the motion of a viscous compressible barotropic fluid in 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.1991 Mathematics Subject Classification: 35A05, 35R35, 76N10.

How to cite

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Wojciech M. Zajączkowski. On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1993. <http://eudml.org/doc/219354>.

@book{WojciechM1993,
abstract = {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.1991 Mathematics Subject Classification: 35A05, 35R35, 76N10.},
author = {Wojciech M. Zajączkowski},
keywords = {free boundary; compressible barotropic viscous fluid; global existence; anisotropic Sobolev spaces; Korn inequality; constant exterior pressure; existence of local-in-time highly regular solutions; existence of global- in-time solutions},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface},
url = {http://eudml.org/doc/219354},
year = {1993},
}

TY - BOOK
AU - Wojciech M. Zajączkowski
TI - On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface
PY - 1993
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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.1991 Mathematics Subject Classification: 35A05, 35R35, 76N10.
LA - eng
KW - free boundary; compressible barotropic viscous fluid; global existence; anisotropic Sobolev spaces; Korn inequality; constant exterior pressure; existence of local-in-time highly regular solutions; existence of global- in-time solutions
UR - http://eudml.org/doc/219354
ER -

Citations in EuDML Documents

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  1. Ewa Zadrzyńska, Wojciech M. Zajączkowski, On local motion of a general compressible viscous heat conducting fluid bounded by a free surface
  2. G. Ströhmer, W. Zajączkowski, Local existence of solutions of the free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids
  3. W. M. Zajączkowski, Existence of local solutions for free boundary problems for viscous compressible barotropic fluids
  4. Ewa Zadrzyńska, Wojciech M. Zajączkowski, On a differential inequality for a viscous compressible heat conducting capillary fluid bounded by a free surface
  5. Piotr Mucha, Wojciech Zajączkowski, On the existence for the Cauchy-Neumann problem for the Stokes system in the L p -framework
  6. Ewa Zadrzyńska, Wojciech M. Zajączkowski, On a differential inequality for equations of a viscous compressible heat conducting fluid bounded by a free surface
  7. Ewa Zadrzyńska, Wojciech M. Zajączkowski, On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting fluid
  8. Ewa Zadrzyńska, Wojciech Zajączkowski, On nonstationary motion of a fixed mass of a viscous compressible barotropic fluid bounded by a free boundary
  9. Ewa Zadrzyńska, On nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary

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