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

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

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topWojciech 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

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