Global Carleman inequalities for Stokes and penalized Stokes equations
Mehdi Badra - Laboratoire LMA, UMR CNRS 5142, Université de Pau et des Pays de l’Adour, 64013 Pau Cedex, France (email)
Abstract: In this note we use the result of  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.
Keywords: Null controllability, penalized Stokes and Oseen equations, global Carleman inequality.
Received: November 2010; Revised: March 2011; Available Online: June 2011.
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