Space-time $L^2$-estimates and life span of the Klainerman-Machedon radial solutions to some semi-linear wave equations

Abstract

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.