Hölder continuity in time for SG hyperbolic systems

We investigate well posedness of the Cauchy problem for SG hyperbolic systems with non-smooth coefficients with respect to time. By assuming the coefficients to be Hölder continuous we show that this low regularity has a considerable influence on the behavior at infinity of the solution as well as on its regularity. This leads to well posedness in suitable Gelfand–Shilov classes of functions on Rn. A simple example shows the sharpness of our results.