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 mathrm {L}^2_{sigma } ({mathbb {R}}^d). 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 mathrm {L}^{2 , nu } ({mathbb {R}}^d) with 0 le nu < 2.