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Partant du principe de conservation de la masse et du principe
fondamental de la dynamique, on retrouve
l'équation d'Euler nous permettant de décrire les modèles
asymptotiques de propagation d'ondes dans des eaux peu profondes
en dimension 1. Pour décrire la propagation des ondes en dimension
2, Kadomtsev et Petviashvili [ 15 (1970) 539] utilisent une perturbation
linéaire de l'équation de KdV. Mais cela ne précise pas si les
équations ainsi obtenues dérivent de l'équation d'Euler, c'est ce
que...
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
The control of the surface of water in a long canal by
means of a wavemaker is investigated. The fluid motion is governed
by the Korteweg-de Vries equation in Lagrangian coordinates.
The null controllability of the elevation of the fluid surface
is obtained thanks to a Carleman estimate and some weighted inequalities.
The global uncontrollability is also established.
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