Volume 23, Number 3, July-September 2017
|Page(s)||1179 - 1200|
|Published online||12 May 2017|
Lagrangian controllability of inviscid incompressible fluids: a constructive approach∗
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.
Received: 7 May 2015
Revised: 26 May 2016
Accepted: 8 June 2016
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.
Mathematics Subject Classification: 35J05 / 35Q93 / 32E30 / 76B75
Key words: Euler equation / Lagrangian controllability
© EDP Sciences, SMAI 2017
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