Stokes and Navier–Stokes Equations with Robin Boundary Conditions in a Half-Space

Abstract.

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 H^∞-calculus on $L_\sigma ^q (\mathbb{R}_ + ^n ).$ As an application we prove also a local existence result for the nonlinear initial value problem of the Navier–Stokes equations with Robin boundary conditions.