# Stokes and Navier-Stokes equations with Robin boundary conditions in a half-space

Preprint Series # 633
Saal, Juergen Stokes and Navier-Stokes equations with Robin boundary conditions in a half-space. (2004);

We study the initial-boundary value problem for the Stokes equations with Robin boundary conditions in the half-space $\mathbb R^n_+$. It is proved that the associated Stokes operator is sectorial and admits a bounded \HIC{} on $L^q_\sigma(\mathbb R^n_+)$. As an application we prove also a local existence result for the nonlinear initial value problem of the Navier-Stokes equations with \RBC.