Journal of the Mathematical Society of Japan

Weak Neumann implies $H^\infty$ for Stokes

Matthias GEIßERT and Peer Christian KUNSTMANN

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Let $\Omega\subset {\mathbb R}^n$ be a domain with uniform $C^3$ boundary and assume that the Helmholtz decomposition exists in ${\mathbb L}^q(\Omega):=L^q(\Omega)^n$ for some $q\in(1,\infty)$. We show that a suitable translate of the Stokes operator admits a bounded ${\cal H}^\infty$-calculus in ${\mathbb L}_\sigma^p(\Omega)$ for $p\in(\min\{q,q'\},\max\{q,q'\})$. For the proof we use a recent maximal regularity result for the Stokes operator on such domains ([GHHS12]) and an abstract result for the ${\cal H}^\infty$-calculus in complemented subspaces ([KKW06], [KW13]).

Article information

J. Math. Soc. Japan Volume 67, Number 1 (2015), 183-193.

First available in Project Euclid: 22 January 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 47A60: Functional calculus

Stokes operator $H^\infty$-functional calculus general unbounded domains Helmholtz decomposition fractional powers


GEIßERT, Matthias; KUNSTMANN, Peer Christian. Weak Neumann implies $H^\infty$ for Stokes. J. Math. Soc. Japan 67 (2015), no. 1, 183--193. doi:10.2969/jmsj/06710183.

Export citation