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.
| Original language | English |
|---|---|
| Pages (from-to) | 657-745 |
| Number of pages | 89 |
| Journal | Journal of the European Mathematical Society |
| Volume | 20 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Jan 2018 |
Keywords
- Capillarity (surface tension)
- Controllability
- Ingham inequality
- Paradifferential calculus
- Water waves