Journal of the European Mathematical Society

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Volume 20, Issue 3, 2018, pp. 657–745
DOI: 10.4171/JEMS/775

Published online: 2018-02-13

Control of water waves

Thomas Alazard[1], Pietro Baldi[2] and Daniel Han-Kwan[3]

(1) École Normale Supérieure, Paris, France
(2) Università di Napoli Federico II, Italy
(3) École Polytechnique, Palaiseau, France

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.

Keywords: Controllability, water waves, capillarity (surface tension), Ingham inequality, paradifferential calculus

Alazard Thomas, Baldi Pietro, Han-Kwan Daniel: Control of water waves. J. Eur. Math. Soc. 20 (2018), 657-745. doi: 10.4171/JEMS/775