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. 657–745DOI 10.4171/JEMS/775