Abstract
We consider two- and three-dimensional gravity and gravity-capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves like a dipole at infinity and obtain a related asymptotic formula for the free surface. We then prove an identity relating the “dipole moment” to the kinetic energy. This implies that the leading-order terms in the asymptotics are nonvanishing and in particular that the angular momentum is infinite. Lastly we prove that the “excess mass” vanishes.
| Original language | English |
|---|---|
| Pages (from-to) | 1941-1956 |
| Number of pages | 16 |
| Journal | Communications on Pure and Applied Mathematics |
| Volume | 71 |
| Issue number | 10 |
| Early online date | 16 Aug 2018 |
| DOIs | |
| Publication status | Published - 31 Oct 2018 |
Acknowledgements
The author thanks Dennis Kriventsov for many helpful discussions on the proof of Theorem 2.1, as well as the two referees for helpful comments and suggestions, some of which led to inclusion of Appendix B.Funding
This research was supported by the National Science Foundation under Award No. DMS-1400926.
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics