On the relation between the large time behavior of the stokes semigroup and the decay of steady stokes flow at infinity

Abstract

Let e -tA be the Stokes semigroup over an unbounded domain O. For construction of the Navier-Stokes flow globally in time, it is crucial to derive Lq-Lr decay estimate (1.4) for ?e -tA; thus, given O, we need to ask which (q, r) admits (1.4). The present paper provides a principle which interprets how this question is related to spatial decay properties of steady Stokes flow in the domain O under consideration.