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A note on the null condition for quadratic nonlinear Klein‐Gordon systems in two space dimensions
Author(s) -
Katayama Soichiro,
Ozawa Tohru,
Sunagawa Hideaki
Publication year - 2012
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21392
Subject(s) - mathematics
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.