Maximal \(L_{p}-L_{q}\) regularity of the linearized initial-boundary value problem for motion of compressible viscous fluids (Q543922)

The author studies an initial-boundary value problem associated with the linearized system of equations which describes the motions of a compressible viscous barotropic fluid in a bounded domain \(\Omega\) of \({\mathbb R}^n\) with Navier boundary conditions. He proves that this problem has a unique global in time solution \((\rho,\vec u)\) in the anisotropic Sobolev space \(W^1_q(0,T ;\dot W_p^1)\times (W^{2,1}_{p,q}(\Omega\times (0,T))^n\). He also proves that exponentially weighted \(L_p-L_q\) estimates hold globally in time for the solution.