It is known that the Stokes operator is not well-defined in Lq-spaces for certain unbounded smooth domains unless q = 2. In this paper, we generalize a new approach to the Stokes resolvent problem and to maximal regularity in general un-bounded smooth domains from the three-dimensional case, see , to the n-dimensional one, n ≥ 2, replacing the space Lq, 1 < q < ∞, by L̃q where L̃q = L̃q ∩ L2 for q ≥ 2 and L̃q = Lq + L2 for 1 < q < 2. In particular, we show that the Stokes operator is well-defined in Lq for every unbounded domain of uniform C1,1-type in Rn, n ≥ 2, satisfies the classical resolvent estimate, generates an analytic semigroup and has maximal regularity.
ASJC Scopus subject areas
- 数学 (全般)