Particle trajectories in extreme Stokes waves over infinite depth
Tony Lyons
We investigate the velocity field of fluid particles in an extreme water wave over infinite depth. It is shown that the trajectories of particles within the fluid and along the free surface do not form closed paths over the course of one period, but rather undergo a positive drift in the direction of wave propagation. In addition it is shown that the wave crest cannot form a stagnation point despite the velocity of the fluid particles being zero there.
keywords: weak solution maximum principles particle trajectory. Stokes wave
The 2-component dispersionless Burgers equation arising in the modelling of blood flow
Tony Lyons
This article investigates the properties of the solutions of the dispersionless two-component Burgers (B2) equation, derived as a model for blood-flow in arteries with elastic walls. The phenomenon of wave breaking is investigated as well as applications of the model to clinical conditions.
keywords: breaking waves dispersionless limit. Blood flow nonlinear waves
Two-component higher order Camassa-Holm systems with fractional inertia operator: A geometric approach
Joachim Escher Tony Lyons
In the following we study the qualitative properties of solutions to the geodesic flow induced by a higher order two-component Camassa-Holm system. In particular, criteria to ensure the existence of temporally global solutions are presented. Moreover in the metric case, and for inertia operators of order higher than three, the flow is shown to be geodesically complete.
keywords: global solutions. Diffeomorphism group geodesic flow

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