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 $$\mathrm {L}^2_{\sigma } ({\mathbb {R}}^d)$$ L σ 2 ( R d ) . Such estimates are well-known for elliptic equations in form pointwise heat kernel bounds and systems integrated estimates. On our way to unveil this behavior we prove resolvent Morrey spaces {L}^{2 , \nu , ν $$0 \le < 2$$ 0 ≤ <