Wave attractors in rotating fluids: A paradigm for ill-posed Cauchy problems

In the limit of low viscosity, we show that the amplitude of the modes of o scillation 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 el aborate a scenario for the asymptotic behavior of the eigenmodes and eigens pectrum 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.