TY - JOUR
T1 - Global Well-posedness for the Klein-Gordon Equation Below the Energy Norm
JO - Journal of Partial Differential Equations
VL - 2
SP - 97
EP - 121
PY - 2004
DA - 2004/05
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5380.html
KW - Klein-Gordon equations
KW - Strichartz estimates
KW - Besov spaces
KW - wellposedness
AB -  We study global well-posedness below the energy norm of the Cauchy problem 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.