Counterexamples to $C^{\infty}$ well posedness for some hyperbolic operators with triple characteristics

In this paper we prove that for a class of non-effectively hyperbolic operators with smooth triple characteristics the Cauchy problem is well posed in the Gevrey 2 class, beyond the generic Gevrey class $3/2$ (see e.g. \cite{Bro}). Moreover we show that this value is optimal.

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