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Optimal control of the Primitive Equations of the Ocean with Lagrangian observations

Maëlle Nodet 1
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019], LJK [2007-2015] - Laboratoire Jean Kuntzmann [2007-2015], Inria Grenoble - Rhône-Alpes
Abstract : We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. The observation operator maps a solution of the Primitive Equations to the trajectory of a Lagrangian particle. This paper proves the existence of an optimal control for the regularized problem. To do that, we prove also new energy estimates for the Primitive Equations, thanks to well-chosen functional spaces, which distinguish the vertical dimension from the horizontal ones. We illustrate the result with a numerical experiment.
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Maëlle Nodet. Optimal control of the Primitive Equations of the Ocean with Lagrangian observations. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2010, 16 (2), pp.400-419. ⟨10.1051/cocv/2009003⟩. ⟨inria-00268804v2⟩

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