Control of water waves
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: MSRI: Simons Auditorium
water waves in a tank
generating water waves
finite boundary condition
76B15 - Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]
35A01 - Existence problems: global existence, local existence, non-existence
35B30 - Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]
Water waves are disturbances of the free surface of a liquid. They are, in general, produced
by the immersion of a solid body or by impulsive pressures applied on the free surface. The
two questions we discuss in this talk are the following:
- which waves can be generated by blowing on a localized portion of the free surface ?
Our main result with Pietro Baldi and Daniel Han-Kwan asserts that one can generate any small amplitude, periodic in x, two-dimensional, gravity-capillary water waves.
- consider now gravity water waves in a rectangular tank. Is-it possible to estimate their energy by
looking only at the motion of some of the curves of contact between the free surface and the vertical walls
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