On the Lp–Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domain |
| |
Authors: | Rieko Shimada |
| |
Institution: | Department of Mathematical Sciences, School of Science and Engineering, Waseda University, Ohkubo 3‐4‐1, Shinjuku‐ku, Tokyo 169‐8555, JapanDepartment of Mathematical Sciences, School of Science and Engineering, Waseda University, Ohkubo 3‐4‐1, Shinjuku‐ku, Tokyo 169‐8555, Japan=== |
| |
Abstract: | We obtain the Lp–Lq maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ?n (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. |
| |
Keywords: | Stokes equation Robin boundary condition |
|
|