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

Navier-Stokes equations are investigated in a functional setting in 3D open sets $\Omega$, bounded or not, without assuming any regularity of the boundary $\partial\Omega$. 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.

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Published 1 January 2006