Wednesday 18h April 2006
Laboratoire de Météorologie Dynamique / ENS
Room 316, 3rd floor, TAO Dept.
24 rue Lhomond
75252 PARIS CEDEX 05

Seminar: Some Recent Results on Controlability of Fluids and Data Assimilation
by Jean-Claude PUEL, Laboratoire de Mathématiques Appliquées, UVSQ

Résumé

In this presentation, I will explain the notion of trajectories controlability for dissipative and irreversible evolving systems. I will show recent results obtained for the Navier-Stockes equations and also for the coupling with diffusion-convection equations. These results are based on "complicated estimations", also called "Carleman global estimations", which allow to obtain a so-calles observability inequality. Concerning Data Assimilation, if the goal is to recover the state at the final measurement time (unlike the initial time for variational assimilation), this inequality can be seen as a stability inequation. This helps to show that the final state recovering is a well-posed problem. It also helps to show that the minimization of the difference between solution and measurements (with respect to the trajectories - not the initial data) has a solution in a function family eventualy without any initial data. At the cost of a regularity hypothesis on this minimum, the convergence of Tychonov regularized methods is explained.

For more information: J.-C. PUEL (J.-C. Puel email)

Link to presentation: pdf file

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