Navier-Stokes equations in arbitrary domains: The Fujita-Kato scheme

摘要

Navier-Stokes equations are investigated in a functional setting in 3D open sets Omega, bounded or not, without assuming any regularity of the boundary partial derivative Omega. The main idea is to find a correct definition of the Stokes operator in a suitable Hilbert space of divergence-free vectors and apply the Fujita-Kato method, a fixed point procedure, to get a local strong solution.