On local motion of a compressible barotropic viscous fluid with the boundary slip condition (Q1130190)

The authors consider the title problem in a bounded domain \(\Omega\subset \mathbb{R}^3\). By reformulating the problem in Lagrangian coordinates and using a priori estimates in Sobolev-Slobodetski spaces, they prove for sufficiently small \(T>0\) existence of solution such that \(\nu\in W^{2+ \alpha,1+\alpha/2}_2(\Omega^T)\), \(\rho\in W^{1+ \alpha,1/2+ \alpha/2}_2(\Omega^T)\), \(\alpha> 0\), \(\Omega^T= \Omega\times (0,T)\).