On $$L^\infty $$ L ∞ -BMO estimates for derivatives of the Stokes semigroup

Abstract

We consider the Stokes equations in a class of domains that we will call admissible domains including bounded domains, the half space and exterior domains. We will prove new \(L^\infty \) estimates for derivatives of velocity and pressure. The estimates will be given in terms of a BMO-type norm of the initial data.