## Differential and Integral Equations

### 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.

#### Article information

Source
Differential Integral Equations, Volume 19, Number 9 (2006), 961-980.

Dates
First available in Project Euclid: 21 December 2012

Hidano, K.; Yokoyama, K. Space-time $L^2$-estimates and life span of the Klainerman-Machedon radial solutions to some semi-linear wave equations. Differential Integral Equations 19 (2006), no. 9, 961--980. https://projecteuclid.org/euclid.die/1356050327