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

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

2005-11-08

arxiv.org/abs/math/0511213v1

Mathematics

Analysis of PDEs

5 pages

Scientific paper

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