Differential and Integral Equations

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

K. Hidano and K. Yokoyama

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050327

Mathematical Reviews number (MathSciNet)
MR2262091

Zentralblatt MATH identifier
1212.35316

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35B45: A priori estimates 35L15: Initial value problems for second-order hyperbolic equations

Citation

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


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