Global Well-posedness for the Klein-Gordon Equation Below the Energy Norm

Abstract

" We study global well-posedness below the energy norm of the Cauchy problem for the Klein-Gordon equation in R^n with n \u2265 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."