Two-component equations modelling water waves with constant vorticity

Abstract

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.

24 pages

References in corpus (4)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• On an integrable two-component Camassa-Holm shallow water system
• Water Waves and Integrability
• The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations

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• Two-component higher order Camassa-Holm systems with fractional inertia operator: a geometric approach
• Surface waves over currents and uneven bottom
• Geometrical demonstration for persistence properties for a bi-Hamiltonian shallow water system
• A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa-Holm system
• Relational space-time and de Broglie waves