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Licensed Unlicensed Requires Authentication Published by De Gruyter October 5, 2011

Weak Neumann implies Stokes

Matthias Geissert, Horst Heck, Matthias Hieber and Okihiro Sawada

Abstract

Consider a domain Ω ⊂ ℝn with possibly non compact but uniform C3-boundary and assume that the Helmholtz projection P exists on Lp(Ω) for some 1 < p < ∞. It is shown that the Stokes operator in Lp(Ω) generates an analytic semigroup on admitting maximal Lq-Lp-regularity. Moreover, for there exists a unique local mild solution to the Navier–Stokes equations on domains of this form provided p > n.

Received: 2010-02-26
Revised: 2010-09-01
Published Online: 2011-10-05
Published in Print: 2012-08

©[2012] by Walter de Gruyter Berlin Boston