The solvability of the initial boundary-value problem for equations of motion of a viscous compressible barotropic liquid in the spacesW 2 l+1,l/2+1 (Q T )

A new method of estimating the solutions of the Navier-Stokes equations for a viscous compressible barotropic fluid in a bounded domain Ω⊂ℝ³ is suggested, which makes it possible to investigate the problem for the whole scale of anisotropic spaces W ₂ ^l+2,l/2+1 (Q_T), Q_T=Ω×(0,T), for arbitrary l>1/2. Bibliography: 10 titles. To dear Olga Alexandrovna Ladyzenskaya on her jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 200, 1992, pp. 177–186. Translated by V. A. Solonnikov.