REGULARITY CRITERIA FOR WEAK SOLUTIONS OF THE NAVIER-STOKES SYSTEM IN GENERAL UNBOUNDED DOMAINS

We consider weak solutions of the instationary Navier-Stokes system in general unbounded smooth domains Omega subset of R-3 and discuss several criteria to prove that the weak solution is locally or globally in time a strong solution in the sense of Serrin. Since the usual Stokes operator cannot be de fined on all types of unbounded domains we have to replace the space L-q (Omega), q > 2, by (L) over tilde (q) (Omega) = L-q (Omega) boolean AND L-2 (Omega) and Serrin's class L-r (0, T; L-q (Omega)) by L-r (0, T; (L) over tilde (q) (Omega)) where 2 < r < infinity, 3 < q < infinity and 2/r + 3/q = 1.