Geodesic
On the existence for the Dirichlet problem for the compressible linearized Navier–Stokes system in the $L_p$-framework
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
Annales Polonici Mathematici, Tome 78 (2002) no. 3, pp. 241-260
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The existence of solutions to the Dirichlet problem for the compressible linearized Navier–Stokes system is proved in a class such that the velocity vector belongs to $W^{2,1}_r$ with $r>3$. The proof is done in two steps. First the existence for local problems with constant coefficients is proved by applying the Fourier transform. Next by applying the regularizer technique the existence in a bounded domain is shown.
DOI : 10.4064/ap78-3-3
Keywords: existence solutions dirichlet problem compressible linearized navier stokes system proved class velocity vector belongs proof done steps first existence local problems constant coefficients proved applying fourier transform applying regularizer technique existence bounded domain shown

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 
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     title = {On the existence for the {Dirichlet} problem
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     journal = {Annales Polonici Mathematici},
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Piotr Boguslaw Mucha; Wojciech Zaj/aczkowski. On the existence for the Dirichlet problem
for the compressible linearized Navier–Stokes
system in the $L_p$-framework. Annales Polonici Mathematici, Tome 78 (2002) no. 3, pp. 241-260. doi: 10.4064/ap78-3-3

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