A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions

Details A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions

2011-05-10

arxiv.org/abs/1105.1952v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, R. Xue (2004), we show the global existence of asymptotically free solutions if the initial data are sufficiently small in some weighted Sobolev space. Our proof is based on an algebraic characterization of nonlinearities satisfying the null condition.

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