A note on the pressure of strong solutions to the Stokes system in bounded and exterior domains

We consider the Stokes problem in an exterior domain $\mathrm{\Omega }\subset {\mathbb{R}}^n$ with an external force $\bbf \in L^s(0,T; \bW^{k,, r}(\Omega )), (k\in \N, 1<r<\infty)$\mathrm{.}Inthepresentpaperweshowthatincontrastto$\bu$ the boundary regularity of the pressure can be improved according to the differentiability of $\text{bbf}$ up to order $k$. In particular, this implies that the pressure is smooth with respect to $x\in \mathrm{\Omega }$ if $\text{bbf}$ is smooth with respect to $x\in \mathrm{\Omega }$.