On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids

Piotr Boguslaw Mucha, and Wojciech Zajączkowski. "On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids." Annales Polonici Mathematici 78.3 (2002): 227-239. <http://eudml.org/doc/280610>.

@article{PiotrBoguslawMucha2002,
abstract = {The local existence of solutions for the compressible Navier-Stokes equations with the Dirichlet boundary conditions in the $L_p$-framework is proved. Next an almost-global-in-time existence of small solutions is shown. The considerations are made in Lagrangian coordinates. The result is sharp in the $L_p$-approach, because the velocity belongs to $W^\{2,1\}_r$ with r > 3.},
author = {Piotr Boguslaw Mucha, Wojciech Zajączkowski},
journal = {Annales Polonici Mathematici},
keywords = {local existence; compressible Navier-Stokes equations; almost global solutions; Dirichlet boundary conditions},
language = {eng},
number = {3},
pages = {227-239},
title = {On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids},
url = {http://eudml.org/doc/280610},
volume = {78},
year = {2002},
}

TY - JOUR
AU - Piotr Boguslaw Mucha
AU - Wojciech Zajączkowski
TI - On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids
JO - Annales Polonici Mathematici
PY - 2002
VL - 78
IS - 3
SP - 227
EP - 239
AB - The local existence of solutions for the compressible Navier-Stokes equations with the Dirichlet boundary conditions in the $L_p$-framework is proved. Next an almost-global-in-time existence of small solutions is shown. The considerations are made in Lagrangian coordinates. The result is sharp in the $L_p$-approach, because the velocity belongs to $W^{2,1}_r$ with r > 3.
LA - eng
KW - local existence; compressible Navier-Stokes equations; almost global solutions; Dirichlet boundary conditions
UR - http://eudml.org/doc/280610
ER -