On a generalized resolvent estimate for the Stokes system with Robin boundary condition

摘要

We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the L_q framework (1 < q < ∞) in a domain of R~n (n ≧ 2) that is a bounded domain or the exterior of a bounded domain. The Robin condition consists of two conditions: ν · u = 0 and αu + β(T(u,p)_ν - < T(u,p)_ν, ν > ν) = h on the boundary of the domain with α, β ≧ 0 and α + β = 1, where u denotes a velocity vector, p a pressure, T(u,p) the stress tensor for the Stokes flow, and ν the unit outer normal to the boundary of the domain. It presents the slip condition when β = 1 and the non-slip one when α = 1, respectively.