We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the framework in a domain of () that is a bounded domain or the exterior of a bounded domain. The Robin condition consists of two conditions: and on the boundary of the domain with and , where denotes a velocity vector, a pressure, the stress tensor for the Stokes flow, and the unit outer normal to the boundary of the domain. It presents the slip condition when and the non-slip one when , respectively.
Yoshihiro SHIBATA. Rieko SHIMADA. "On a generalized resolvent estimate for the Stokes system with Robin boundary condition." J. Math. Soc. Japan 59 (2) 469 - 519, April, 2007. https://doi.org/10.2969/jmsj/05920469