Low regularity for the nonlinear Klein–Gordon systems

In this paper, we study the global well-posedness below the energy norm of the Cauchy problem for the Klein–Gordon system in R3R3. We prove the HsHs-global well-posedness with s<1s<1 of the Cauchy problem for the Klein–Gordon system. The method invoked is different from the well-known Bourgain’s method [Jean Bourgain, Refinements of Strichartz’s inequality and applications to 2D-NLS with critical nonlinearity, International Mathematial Research Notices 5 (1998) 253–283].