Geodesic
Optimal control of the primitive equations of the ocean with lagrangian observations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 400-419

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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. We aim to reconstruct the initial state of the ocean from lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between lagrangian observations and their model counterpart, plus a regularization term. This paper proves the existence of an optimal control for the regularized problem. To this end, we also prove 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.

DOI : 10.1051/cocv/2009003
Classification : 35Q35, 49J20, 65K10
Keywords: optimal control, partial differential equations, primitive equations, numerical simulation 
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     author = {Nodet, Ma\"elle},
     title = {Optimal control of the primitive equations of the ocean with lagrangian observations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {400--419},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {2},
     year = {2010},
     doi = {10.1051/cocv/2009003},
     mrnumber = {2654200},
     zbl = {1189.35376},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009003/}
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Nodet, Maëlle. Optimal control of the primitive equations of the ocean with lagrangian observations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 2, pp. 400-419. doi: 10.1051/cocv/2009003

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