Two-component equations modelling water waves with constant vorticity

Abstract

24 pagesInternational audienceIn 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

Surface waves over currents and uneven bottom

“…A method has been developed for the measurement of the strength of the wave-current interaction by Thomas and Klopman (1997). A variety of other aspects has been an active research topic (Teles da Silva and Peregrine, 1988;Constantin and Strauss, 2004;Escher, 2004 and2011;Constantin et al, 2006;Henry, 2013;Johnson, 2015 and2017a,b;Escher et al, 2016). Recent developments in the mathematical aspects of wave-current interactions are presented in the monograph by Constantin (2011).…”

Well-posedness, blow-up phenomena and persistence properties for a two-component water wave system

“…The system (1.1) was recently introduced by Escher et al in [1]. In [1], the authors proved the local wellposedness of (1.1) using a geometrical framework, studied the blow-up scenarios and global strong solutions of (1.1) on the circle.…”

A remark on wave breaking for the Dullin–Gottwald–Holm equation

“…Thus, the map q(·, t) is a diffeomorphism of the real line, which corresponds to the Lagrangian viewpoint in fluid dynamics, and has, for α = 1, a geometric interpretation in infinite-dimensional Riemannian geometry (see the discussions in [31,32]). …”