Reduced and generalized Stokes resolvent equations in asymptotically flat layers. II: \(H_\infty\)-calculus
The author studies the generalized Stokes resolvent equations and proves that they are uniquely solvable if and only if a suitable system of reduced Stokes equations are uniquely solvable. The reduced system fits well into the general calculus of parameter-dependent pseudodifferential boundary value problems developed by Grubb in 1966. The calculus here developed is used to construct a parametrix to the reduced Stokes system, which coincides with the exact solution operator modulo term which decay faster as \(|\lambda|\to\infty\). Using this parametrix it is proved that the usual Stokes operator in the Dirichlet case and the reduced Stokes operator in the mixed case admit a bounded \(H_\infty\)-calculus in the sense of McIntosh. A nonsmooth version of parameter dependent Green operators is considered, too.
scientific article; zbMATH DE number 2176391