On the existence for the Dirichlet problem for the compressible linearized Navier–Stokes system in the $L_p$-framework
Volume 78 / 2002
Annales Polonici Mathematici 78 (2002), 241-260
MSC: 35Q30, 76Q10.
DOI: 10.4064/ap78-3-3
Abstract
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.
