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Contrôle en mécanique des fluides et couches limites

Abstract : This thesis is devoted to the study of the controllability of non linear partial differential equations in fluid mechanics. We are mostly interested in Burgers equation and Navier-Stokes equation. Our main goal is to prove small-time global results, even in the presence of boundary layers. We prove that it is possible to obtain such results by introducing a new method named: “well prepared dissipation”. This method proceeds in two phases: first, a quick phase using the inviscid behavior of the system, then a longer phase during which the boundary layer dissipates all by itself. Both for Burgers and for Navier-Stokes with Navier slip-with-friction boundary conditions, we prove that this dissipation is sufficient if it has been well prepared. Moreover, we study a question of local null controllability for the Burgers equation with a single scalar control. We prove by enhancing a second order kernel approach that the system is not small time locally null controllable.
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https://hal.archives-ouvertes.fr/tel-01434170
Contributor : Frédéric Marbach <>
Submitted on : Friday, January 13, 2017 - 11:22:08 AM
Last modification on : Thursday, March 26, 2020 - 9:14:17 PM
Long-term archiving on: : Friday, April 14, 2017 - 7:40:01 PM

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  • HAL Id : tel-01434170, version 1

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Frédéric Marbach. Contrôle en mécanique des fluides et couches limites. Optimisation et contrôle [math.OC]. Université Pierre et Marie Curie (UPMC, Paris 6), 2016. Français. ⟨tel-01434170v1⟩

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