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

DOI Web Site 10 Citations 30 References
  • Shibata Yoshihiro
    Department of Mathematical Sciences, School of Science and Engineering, Waseda University
  • Shimada Rieko
    Department of Mathematical Sciences, School of Science and Engineering, Waseda University

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We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the Lq framework (1 < q < ∞) in a domain of Rn (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.

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