INSTABILITY OF THE CAUCHY-KOVALEVSKAYA SOLUTION FOR A CLASS OF NONLINEAR SYSTEMS
Résumé
We prove that in any C∞-neighborhood of an analytic Cauchy datum, there exists a
smooth function such that the corresponding initial value problem does not have any classical
solution for a class of first-order nonlinear systems. We use a method initiated by G. M´etivier for
elliptic systems based on the representation of solutions and on the FBI transform; in our case the
system can be hyperbolic at initial time, but the characteristic roots leave the real line at positive
times.