SPACE-TIME L2-ESTIMATES AND LIFE SPAN OF THE KLAINERMAN-MACHEDON RADIAL SOLUTIONS TO SOME SEMI-LINEAR WAVE EQUATIONS

摘要

We consider the Cauchy problem for some semi-linear wave equations in three space dimensions and prove global or almost global existence of the Klainerman-Machedon radial solutions. The proof is carried out by a contraction-mapping argument based on a refined version of the Keel-Smith-Sogge estimate, together with the Morawetz-type inequality.