On Oseen resolvent estimates. (English) Zbl 1240.35381

Deuring, Paul; Varnhorn, Werner

Differ. Integral Equ. 23, No. 11-12, 1139-1149 (2010).

Summary: 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.

MSC:

35Q30	Navier-Stokes equations
76D03	Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D07	Stokes and related (Oseen, etc.) flows

Keywords:

Oseen system; resolvent estimate