ON SOME GEOMETRY OF PROPAGATION IN DIFFRACTIVE TIME SCALES

Christophe Cheverry (1) , Thierry Paul (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 CMLS - Centre de Mathématiques Laurent Schwartz

In this article, we develop a non linear geometric optics which presents the two main following features. It is valid in diffractive times and it extends the classical approaches to the case of fast variable coefficients. In this context, we can show that the energy is transported along the rays associated with some non usual long-time hamiltonian. Our analysis needs structural assumptions and initial data suitably polrarized to be implemented. All the required conditions are met concerning a current model arising in fluid mechanics and which was the original motivation of our work. As a by product, we get results complementary to the litterature concerning the propagation of the Rossby waves which play a part in the description of large oceanic currents, like Gulf stream or Kuroshio.

Mots clés: Hyperbolic systems; singularities; diffractive nonlinear geometric optics; geophysical flows

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Cheverry, Thierry Paul. ON SOME GEOMETRY OF PROPAGATION IN DIFFRACTIVE TIME SCALES. Discrete and Continuous Dynamical Systems - Series A, 2012, 32 (2), pp.Pages: 499 - 538. ⟨10.3934/dcds.2012.32.499⟩. ⟨hal-00514861⟩