Strong solvability of the Stokes and Navier-Stokes equations in weak $L^{n}$ space (The structure of function spaces and its environment)

Abstract

In this résumé we investigate the strong soluvability of the Stokes and the Navier Stokes equations in weak L^{n}-space, where the Stokes semigroup is analytic but not strongly continuous at t=0. More precisely, the local in time strong solvability is concerned. To construct a strong solution of the Naiver-Stokes equations in weak L^{n}-space, we clarify the condition on the external forces, which is inherited from the strong solvability of the inhomogeneous Stokes equations. This résumé is based on the joint work with Professor Yohei Tsutsui.