Mathematical Control and Related Fields (MCRF)

Global Carleman inequalities for Stokes and penalized Stokes equations

Pages: 149 - 175, Volume 1, Issue 2, June 2011      doi:10.3934/mcrf.2011.1.149

       Abstract        References        Full Text (329.8K)       Related Articles       

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 [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.

Keywords:  Null controllability, penalized Stokes and Oseen equations, global Carleman inequality.
Mathematics Subject Classification:  Primary: 93B05, 76D07; Secondary: 93C20, 76D55.

Received: November 2010;      Revised: March 2011;      Available Online: June 2011.