Gevrey well posedness for a second order weakly hyperbolic equation with non regular in time coefficients

Abstract

We consider a second order weakly hyperbolic equation with coefficients depending both on time and space. We assume the coefficients of the equation to have some kind of Hölder behavior with respect to time, and we add for the coefficients of the lower order terms an appropriate Levi condition. We prove Gevrey well posedness of the Cauchy problem for this equation for a small enough Gevrey index.