On Oseen resolvent estimates

Abstract

We consider the resolvent problem for the Oseen system and for the scalar Oseen equation in the whole space $\mathbb{R}^{3}$. It is shown that, for small values of the resolvent parameter, it is impossible to obtain an L$^{2}$-estimate analogous to the one that is valid for the Stokes resolvent, even if the resolvent parameter has positive real part.