Boundary observability of gravity water waves

  • Thomas Alazard

    CNRS et Centre de Mathématiques et de Leurs Applications UMR 8536, École Normale Supérieure de Paris-Saclay, 61 av du Président Wilson, Cachan F-94235, France


Consider a three-dimensional fluid in a rectangular tank, bounded by a flat bottom, vertical walls and a free surface evolving under the influence of gravity. We prove that one can estimate its energy by looking only at the motion of the points of contact between the free surface and the vertical walls. The proof relies on the multiplier technique, the Craig–Sulem–Zakharov formulation of the water-wave problem, a Pohozaev identity for the Dirichlet to Neumann operator, previous results about the Cauchy problem and computations inspired by the analysis done by Benjamin and Olver of the conservation laws for water waves.

Cite this article

Thomas Alazard, Boundary observability of gravity water waves. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 3, pp. 751–779

DOI 10.1016/J.ANIHPC.2017.07.006