Global Carleman inequalities for Stokes and penalized Stokes equations

Mehdi Badra

doi:10.3934/mcrf.2011.1.149

Article Contents

2011, Volume 1, Issue 2: 149-175. Doi: 10.3934/mcrf.2011.1.149

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Global Carleman inequalities for Stokes and penalized Stokes equations

Mehdi Badra^1,

1.
Laboratoire LMA, UMR CNRS 5142, Université de Pau et des Pays de l’Adour, 64013 Pau Cedex

Received: October 31, 2010

Revised: February 28, 2011

Published: May 2011

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Abstract

In this note we use the result of [22] to prove a global Carleman inequality related to the null controllability of penalized Stokes kind systems. The constants of the obtained Carleman inequality are uniform in terms of the penalization parameter $\varepsilon$. It then provides a null control with a uniformly (in $\varepsilon$) bounded $L^2$ norm. With a limiting argument we also deduce a new Carleman inequality for Stokes type system. Thus, we apply theses results to obtain the null controllability of Oseen and Navier-Stokes system in the penalized and in the non penalized cases.

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Mathematics Subject Classification: Primary: 93B05, 76D07; Secondary: 93C20, 76D55.

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