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

Sylvie Monniaux
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Abstract

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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Sylvie Monniaux. 2005-11-08. Navier-Stokes equations in arbitrary domains : the Fujita-Kato scheme. https://arxiv.org/abs/math/0511213

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