On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids
Volume 78 / 2002
Annales Polonici Mathematici 78 (2002), 227-239
MSC: 35Q30, 76Q10.
DOI: 10.4064/ap78-3-2
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 $r>3$.
