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

12 pages