$H^{\infty}$-calculus for a system of Laplace operators with mixed order boundary conditions

Matthias Geissert; Horst Heck; Christof Trunk

doi:10.3934/dcdss.2013.6.1259

Article Contents

2013, Volume 6, Issue 5: 1259-1275. Doi: 10.3934/dcdss.2013.6.1259

This issue Previous Article Existence and uniqueness of time-periodic solutions to the Navier-Stokes equations in the whole plane Next Article A remark on a Liouville problem with boundary for the Stokes and the Navier-Stokes equations

$H^{\infty}$-calculus for a system of Laplace operators with mixed order boundary conditions

1.
TU Darmstadt, FB Mathematik, Schlossgartenstr 7, D-64289 Darmstadt

Received: December 31, 2011

Revised: January 31, 2012

Published: September 2013

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Abstract

In this paper we prove that the $L^p$ realisation of a system of Laplace operators subjected to mixed first and zero order boundary conditions admits a bounded $H^{\infty}$-calculus. Furthermore, we apply this result to the Magnetohydrodynamic equation with perfectly conducting wall condition.

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Mathematics Subject Classification: Primary: 35K51; Secondary: 76W05.

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