Abstract: We consider maximal regularity for the Stokes system in the half Euclidian space under the stress boundary condition. Many of results were devoted to the Navier-Stokes equations with the free boundary problem such as an ocean problem. We consider time L^1 maximal regularity related to the nonlinear free boundary problem and show critical conditions for the initial, external and boundary data to the linear Stokes problem. This talk is based on a joint work with Prof. Senjo Shimizu (Kyoto University).
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