GLOBAL WELL-POSEDNESS FOR THE KLEIN-GORDON EQUATION BELOW THE ENERGY NORM

We study global well-posedness below the energy norm of the Cauchyproblem for the Klein-Gordon equation in R^n with n≥3. By means of Bourgain‘s method along with the endpoint Strichartz estimates of Keel and Tao, we prove the H^s-global well-posedness with s<1 of the Cauchy problem for the Klein-Gordon equation. This we do by establishing a series of nonlinear a priori estimates in the setting of Besov spaces.