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

Maëlle Nodet

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 16, Issue: 2, page 400-419
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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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 16.2 (2010): 400-419. <http://eudml.org/doc/250732>.

@article{Nodet2010,
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. 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. },
author = {Nodet, Maëlle},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; partial differential equations; Primitive Equations; numerical simulation; optimal control; primitive equations},
language = {eng},
month = {4},
number = {2},
pages = {400-419},
publisher = {EDP Sciences},
title = {Optimal control of the Primitive Equations of the ocean with Lagrangian observations},
url = {http://eudml.org/doc/250732},
volume = {16},
year = {2010},
}

TY - JOUR
AU - Nodet, Maëlle
TI - Optimal control of the Primitive Equations of the ocean with Lagrangian observations
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/4//
PB - EDP Sciences
VL - 16
IS - 2
SP - 400
EP - 419
AB - 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.
LA - eng
KW - Optimal control; partial differential equations; Primitive Equations; numerical simulation; optimal control; primitive equations
UR - http://eudml.org/doc/250732
ER -

References

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