Contrôlabilité d'équations issues de la mécanique des fluides

Abstract : In this work we study the global controllability of some nonlinear equations of fluid mechanics, namely Burgers type equations, a Korteweg-de Vries equation and a 2-D Navier-Stokes system. The strategy consists in both using the return method of J.-M. Coron and playing on the nonlinearity of the equation.
In this way, we prove in the first part the global exact controllability of nonviscous Burgers type equations, for any positive time. We then use this result to obtain a global approximate controllability result for the viscous Burgers equation. This property, added to a local controllability result gives the global controllability of the viscous Burgers equation for any positive time.
In the second part, we obtain in a similar way the global exact controllability of a nonlinear Korteweg-de Vries equation, for any positive time.
Finally, in the last part, we use the same strategy and results on the Euler equation for inviscid fluids to obtain the global null controllability of a 2-D Navier-Stokes system with Navier slip boundary conditions, for any positive time.
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Submitted on : Sunday, July 26, 2009 - 7:57:05 PM
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Marianne Chapouly. Contrôlabilité d'équations issues de la mécanique des fluides. Mathématiques [math]. Université Paris Sud - Paris XI, 2009. Français. ⟨tel-00407569⟩

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