BOUNDED H-infinity-CALCULUS FOR THE HYDROSTATIC STOKES OPERATOR ON L-p-SPACES AND APPLICATIONS

摘要

It is shown that the hydrostatic Stokes operator on Lp/sigma (Omega), where Omega subset of R-3 is a cylindrical domain subject to mixed periodic, Dirichlet and Neumann boundary conditions, admits a bounded H-infinity- calculus on Lp/sigma(Omega) for p is an element of( 1,infinity) of H-infinity- angle 0. In particular, maximal L-q - L-p-regularity estimates for the linearized primitive equations are obtained.