Geodesic
Lagrangian controllability of inviscid incompressible fluids: a constructive approach
Horsin, Thierry1  ; Kavian, Otared2 
1 CNAM, Laboratoire M2N EA7340, 292 rue Saint-Martin, Case 2D5000, 75003 Paris, France.
2 Université de Versailles Saint-Quentin; Laboratoire de Mathématiques de Versailles (UMR 8100), 45 avenue des Etats-Unis 78030 Versailles cedex, France.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1179-1200

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We present here a constructive method of Lagrangian approximate controllability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of formal computations in the framework of explicit Runge approximations of holomorphic functions by rational functions, or an approach based on the study of the range of an operator by showing a density result. For this last insight in view of numerical simulations in progress, we analyze through a simplified problem the observed instabilities.

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DOI : 10.1051/cocv/2016043
Classification : 35J05, 35Q93, 32E30, 76B75
Keywords: Euler equation, Lagrangian controllability

Horsin, Thierry 1 ; Kavian, Otared 2

1 CNAM, Laboratoire M2N EA7340, 292 rue Saint-Martin, Case 2D5000, 75003 Paris, France.
2 Université de Versailles Saint-Quentin; Laboratoire de Mathématiques de Versailles (UMR 8100), 45 avenue des Etats-Unis 78030 Versailles cedex, France. 
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     title = {Lagrangian controllability of inviscid incompressible fluids: a constructive approach},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1179--1200},
     publisher = {EDP-Sciences},
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Horsin, Thierry; Kavian, Otared. Lagrangian controllability of inviscid incompressible fluids: a constructive approach. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 1179-1200. doi: 10.1051/cocv/2016043

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