JournalsjemsVol. 20, No. 3pp. 657–745

Control of water waves

  • Thomas Alazard

    École Normale Supérieure, Paris, France

  • Pietro Baldi

    Università di Napoli Federico II, Italy

  • Daniel Han-Kwan

    École Polytechnique, Palaiseau, France
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Abstract

We prove local exact controllability in arbitrarily short time of the two-dimensional incompressible Euler equation with free surface, in the case with surface tension. This proves that one can generate arbitrarily small amplitude periodic gravity-capillary water waves by blowing on a localized portion of the free surface of a liquid.

Cite this article

Thomas Alazard, Pietro Baldi, Daniel Han-Kwan, Control of water waves. J. Eur. Math. Soc. 20 (2018), no. 3, pp. 657–745

DOI 10.4171/JEMS/775