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.
|Number of pages||16|
|Journal||Communications on Pure and Applied Mathematics|
|Publication status||E-pub ahead of print - 16 Aug 2018|
ASJC Scopus subject areas
- Applied Mathematics