On the Lp–Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domain
Rieko Shimada · Mathematical Methods in the Applied Sciences · 2006
Abstract We obtain the Lp–Lq maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ℝn (n⩾2). The Robin condition consists of two conditions: v ⋅ u=0 and αu+β(T(u, p)v – 〈T(u, p)v, v〉v)=h on the boundary of the domain with α, β⩾0 and α+β=1, where u and p denote a velocity vector and a pressure, T(u, p) the stress tensor for the Stokes flow and v the unit outer normal to the boundary of the domain. It presents the slip condition when β=1 and non‐slip one when α=1, respectively. The slip condition is appropriate for problems that involve free boundaries. Copyright © 2006 John Wiley & Sons, Ltd.