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
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DOI：
10.1002/cpa.21392
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发表时间：
2011-05
影响因子：
3
通讯作者：
S. Katayama;T. Ozawa;Hideaki Sunagawa
中科院分区：
文献类型：
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作者：
S. Katayama;T. Ozawa;Hideaki Sunagawa
考虑二维空间中质量满足共振关系的二次非线性Klein-Gordon系统的Cauchy问题。在零条件下，在J. -M. Delort，D. Fang和R. Xue（J. Funct. Anal. 211（2004），no. 2，288-323），我们证明了在某些加权Sobolev空间中，当初始数据足够小时，渐近自由解的整体存在性。我们的证明是基于满足零条件的非线性代数特征。© 2012 Wiley Periodicals，Inc.
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, and R. Xue (J. Funct. Anal. 211 (2004), no. 2, 288–323), 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. © 2012 Wiley Periodicals, Inc.