Geodesic
On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids
Piotr Boguslaw Mucha1 ; Wojciech Zaj/aczkowski2
1 Institute of Applied Mathematics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-950 Warszawa, Poland and Institute of Mathematics and Operations Research Military University of Technology Kaliskiego 2 01-489 Warszawa, Poland
Annales Polonici Mathematici, Tome 78 (2002) no. 3, pp. 227-239.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $r>3$.
DOI : 10.4064/ap78-3-2
Keywords: local existence solutions compressible navier stokes equations dirichlet boundary conditions p framework proved almost global in time existence small solutions shown considerations made lagrangian coordinates result sharp p approach because velocity belongs

Piotr Boguslaw Mucha 1 ; Wojciech Zaj/aczkowski 2

1 Institute of Applied Mathematics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland
2 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 00-950 Warszawa, Poland and Institute of Mathematics and Operations Research Military University of Technology Kaliskiego 2 01-489 Warszawa, Poland 
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     title = {On local-in-time existence for the {Dirichlet} problem
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Piotr Boguslaw Mucha; Wojciech Zaj/aczkowski. On local-in-time existence for the Dirichlet problem
for equations of compressible viscous fluids. Annales Polonici Mathematici, Tome 78 (2002) no. 3, pp. 227-239. doi : 10.4064/ap78-3-2. http://geodesic.mathdoc.fr/articles/10.4064/ap78-3-2/

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