title: Wave attractors in rotating fluids: A paradigm for ill-posed cauchy problems
abstract: In the limit of low viscosity, we show that the amplitude of the modes of oscillation of a rotating fluid, namely inertial modes, concentrate along an attractor formed by a periodic orbit of characteristics of the underlying hyperbolic Poincare equation. The dynamics of characteristics is used to elaborate a scenario for the asymptotic behavior of the eigenmodes and eigenspectrum in the physically relevant regime of very low viscosities which are out of reach numerically. This problem offers a canonical ill-posed Cauchy problem which has applications in other fields.
authors.affiliation: Observatoire Midi-Pyrenees, 14 avenue Edouard Belin, F-31400 Toulouse, France and Institut Universitaire de France.
authors.initials: M
authors.lastname: Rieutord
authors.initials: B
authors.lastname: Georgeot
authors.initials: L
authors.lastname: Valdettaro