Maximal regularity of the Stokes system with Navier boundary condition in general unbounded domains

Abstract

Consider the instationary Stokes system in general unbounded domains $\Omega \subset \mathbb{R}^n$, $n \geq 2$, with boundary of uniform class $C^3$, and Navier slip or Robin boundary condition. The main result of this article is the maximal regularity of the Stokes operator in function spaces of the type $\tilde{L}^q$ defined as $L^q \cap L^2$ when $q \geq 2$, but as $L^q + L^2$ when $1 < q < 2$, adapted to the unboundedness of the domain.