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On some geometry of propagation in diffractive time scales. (English) Zbl 1243.35118

Authors’ abstract: “We develop a nonlinear 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 a 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, which was the original motivation of the authors’ work. As a by product, we obtain results complementary to the literature concerning the propagation of the Rossby waves which play a part in the description of large oceanic currents, like Gulf stream or Kuroshio.”

MSC:

35L60 First-order nonlinear hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
35B25 Singular perturbations in context of PDEs
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