| 概要 | I will talk about the  -sectoriality of the Stokes
operators, which implies the generation of analytic
semigroup and the maximal  - regularity at the
same time. The notion of -sectoriality is related to
the -bound of the operator families, which plays an
important role to use the Weis operator valued Fourier
multiplier theorem. The main assumption on the domain
is the unique solvability of weak Dirichlet-Neumann
problem. According to our theory, a local in time
existence of the Navier-Stokes equations follows from
the unique solvability of weak Dirichlet-Neumann
problem. |