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

2005/11/08 by Monniaux, Sylvie · 1 citation
#35Q30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/0511213

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.

Cited by

• H^∞-calculus for Stokes operators on rough and on unbounded domains

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