Some inverse and control problems for fluids

Fernández-Cara, Enrique; Horsin, Thierry; Kasumba, Henry

Annales mathématiques Blaise Pascal, Tome 20 (2013) no. 1, pp. 101-138.

Ce papier discute quelques problèmes inverses et de contrôle pour des systèmes de type Navier-Stokes. On insiste sur quelques aspects de nature à la fois théorique et numérique ayant menés récemment à des résultats nouveaux : Problèmes inverses géométriques, Contrôlabilité Eulérienne et Lagrangienne, Réduction de tourbillons par optimisation de forme, etc.

This paper deals with some inverse and control problems for the Navier-Stokes and related systems. We will focus on some particular aspects that have recently led to interesting (theoretical and numerical) results: geometric inverse problems, Eulerian and Lagrangian controllability and vortex reduction oriented to shape optimization.

Classification : 35R30, 76B75, 76D55
Mots clés : Navier-Stokes equations, Euler equations, inverse problems, exact and approximate controllability, Lagrangian controllability, vortex reduction, shape optimization

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