Solvability of initial-boundary value problem for the equations of motion of a viscous compressible baratropic fluid in the spaces $W_2^{2+l,1+l/2}(Q_T)$

There is presented a new method of estimates of solutions of the Navier–Stokes equations for a viscous compressible barotropic fluid in a bounded domain $\Omega\subset\mathbb{R}^3$ which makes it possible to investigate the problem in a complete scale of anisotropic spaces $W_2^{2+l,1+l/2}(Q_T)$, $Q_T=\Omega\times(0,T)$ with arbitrary $l>1/2$.