On some geometry of propagation in diffractive time scales

Christophe Cheverry; Thierry Paul

doi:10.3934/dcds.2012.32.499

Article Contents

2012, Volume 32, Issue 2: 499-538. Doi: 10.3934/dcds.2012.32.499

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On some geometry of propagation in diffractive time scales

Christophe Cheverry^1, and
Thierry Paul^2,

1.
UMR6625, Université Rennes 1, Campus de Beaulieu, 263 avenue du Général Leclerc CS 74205, 35042 Rennes
2.
UMR7640, Centre de Mathmatiques Laurent Schwartz, École polytechnique

Received: August 31, 2010

Revised: November 30, 2010

Published: January 2012

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Abstract

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 [7, 17, 18, 24] 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 [2, 3, 8, 9, 10, 11, 19, 21] arising in fluid mechanics, 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.

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Mathematics Subject Classification: Primary: 35L, 35Q; Secondary: 76, 37.

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References

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