On the $L^p$-$L^q$ estimates of the gradient of solutions to the Stokes problem

Abstract

The paper is concerned with estimates of the gradient of the solutions to the Stokes IBVP both in a bounded and in an exterior domain. More precisely, we look for estimates of the kind $\Vert \nabla v(t){\Vert }_q\le g(t)\Vert \nabla v_0{\Vert }_p,q\ge p>1$, for all $t>0$, where function $g$ is independent of $v_0$.

There is an improvement of Proposition1