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

2011/05/10 by Soichiro Katayama, Tohru Ozawa, Katayama, Soichiro +3
Mathematics · #35B40 #35L15 #35L70 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35L15 #msc:35L70

paper · pdf · doi:10.48550/arxiv.1105.1952

18 pages

arxiv created 2011/05/10 · arxiv updated 2011/05/11

Abstract

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.

Related

• Global solution to the wave and Klein-Gordon system under null condition in dimension two
• Global small amplitude solutions for two-dimensional nonlinear Klein-Gordon systems in the presence of mass resonance
• Global existence without decay for quadratic Klein-Gordon equations
• Global solutions to quasilinear wave-Klein-Gordon systems in two space dimensions
• Asymptotic behavior of 2D Wave-Klein-Gordon coupled system under null condition