Two-component equations modelling water waves with constant vorticity
In this paper, we derive a two-component system of nonlinear equations which models 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 criterion for global existence.
Water waves , Vorticity , Model equations , Euler equation , Diffeomorphism group
Escher, J., Henry, D., Kolev, B. and Lyons, T. (2016) 'Two-component equations modelling water waves with constant vorticity', Annali Di Matematica Pura Ed Applicata, 195 (1), pp. 249-271. doi: 10.1007/s10231-014-0461-z
© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2014. This is a post-peer-review, pre-copyedit version of an article published in Annali di Matematica. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10231-014-0461-z