Geodesic
On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids
Piotr Boguslaw Mucha1 ; Wojciech Zaj/aczkowski2
1Institute of Applied Mathematics and Mechanics Warsaw University Banacha 2 02-097 Warszawa, Poland
2Institute 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
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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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     journal = {Annales Polonici Mathematici},
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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

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