Two-component equations modelling water waves with constant vorticity

Joachim Escher (1) , David Henry (2) , Boris Kolev (3) , Tony Lyons (4)

1 IFAM - Institute for Applied Mathematics
2 UCC - Department of Applied Mathematics
3 I2M - Institut de Mathématiques de Marseille
4 DIT - School of Mathematical Sciences

In this paper we derive a two-component system of nonlinear equations which model two-dimensional shallow water waves with constant vorticity. Then we prove well-posedness of this equation using a geometrical framework which allows us to recast this equation as a geodesic flow on an infinite dimensional manifold. Finally, we provide a criteria for global existence.

Mots clés: diffeomorphism group; Water waves; vorticity; model equations; Euler equation

Domaines: Physique mathématique [math-ph]

Joachim Escher, David Henry, Boris Kolev, Tony Lyons. Two-component equations modelling water waves with constant vorticity. Annali di Matematica Pura ed Applicata, 2016, 195 (1), pp.249-271. ⟨10.1007/s10231-014-0461-z⟩. ⟨hal-01002338v2⟩