Liouville theorems for the Stokes equations with applications to large time estimates

Abstract

We study Liouville theorems for the non-stationary Stokes equations in exterior domains in Rn under decay conditions for spatial variables. As applications, we prove that the Stokes semigroup is a bounded analytic semigroup on Lσ∞ of angle π/2 for n≥3. We also prove large time estimates for n=2 with zero net force.