Navier-Stokes' Equation with the Generalized Impermeability Boundary Conditions and Initial Data in Domains of Powers of the Stokes Operator

摘要

We deal with the Navier-Stokes equation with the, generalized impermeability boundary conditions. We give basic information on these boundary conditions and we further study dynamical properties of solutions, like stability, fast decay and similar. The used norms are graph norms of powers of the Stokes operator S.