2009/08/31 by Soichiro Katayama · 1 citation
Mathematics · #math.AP #msc:35L70
paper · pdf · doi:10.1007/s00209-010-0808-0
published as Mathematische Zeitschrift 270 (2012), 487-513 · 31 pages. The final version
arxiv created 2011/11/18 · arxiv updated 2012/01/17
We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null condition on self-interactions between wave equations. Our condition is much weaker than the strong null condition introduced by Georgiev for this kind of coupled system. Consequently our result is applicable to certain physical systems, such as the Dirac-Klein-Gordon equations, the Dirac-Proca equations, and the Klein-Gordon-Zakharov equations.