On mixed boundary value problems for pseudoparabolic systems

Solvability analysis of mixed boundary value problems for pseudoparabolic systems in a special scale of weighted Sobolev spaces is presented. The class under consideration contains the linearized Navier–Stokes system. It is proved that, choosing the power weight, one can diminish the number of solvability conditions and in some cases obtain unconditional solvability of the boundary value problems.