Abstract
The motivation for the present work comes from a study of initialboundary value problems for the Navier-Stokes equations [G-Sl, 2, 33. These problems (or rather, their linearized versions) are degenerate parabolic, and we had found a method to get rid of the degeneracy by carrying the problems over to pseudo-differential non-degenerate parabolic problems, where the results of the book [Gr2] could be used. However, the solvability statements for parabolic problems formulated in [Gr2] could be made more interesting and useful by some extra developments, in particular a deeper analysis of the necessary compatibility conditions and an inclusion of all values of the Sobolev space exponents, also those that have an exceptional role in boundary value problems. Since this study has an interest not only for the Navier-Stokes equations, but also more generally (e.g., whenever a reduction of a differential operator problem leads to a parabolic pseudo-differential boundary value problem), we decided to present it in a separate article. We consider a problem
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