Lack of Gevrey solvability for a model operator

Abstract

We prove that the Cauchy problem for the model hyperbolic operator in ${\mathbb{R}}^4$ \[ Q=-D_t^2+2xD_tD_y+D_x^2+x^3D_y^2+D_z^2+z^2D_y^2 \] is not locally solvable at the origin, in the Gevrey $s$ class if $s>6$.

Withdrawn by the author because an error in the localization argument invalidates the proof of Theorem 1.1. The comparison between temporal growth and the size of the localized Cauchy data is not justified. The claimed Gevrey nonsolvability result is therefore withdrawn