On off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients

Abstract

We investigate off-diagonal decay properties of the generalized Stokes semigroup with bounded measurable coefficients on L2σ(Rd). Such estimates are well-known for elliptic equations in the form of pointwise heat kernel bounds and for elliptic systems in the form of integrated off-diagonal estimates. On our way to unveil this off-diagonal behavior we prove resolvent estimates in Morrey spaces L2,ν(Rd) with 0≤ν<2.