TY - JOUR
T1 - A system of quadratic nonlinear Klein-Gordon equations in 2d
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
N1 - Funding Information:
The work of P.I.N. is partially supported by CONACYT and PAPIIT. One of the authors (N.H.) would like to thank Professor Sunagawa for useful discussion on the subject and information of a related article [9].
PY - 2013/4/15
Y1 - 2013/4/15
N2 - We consider the system of quadratic nonlinear Klein-Gordon equations in two space dimensions. Under the mass condition such that 2m1>m2, we construct the scattering operator in an almost natural weighted Sobolev class H1+δ,1 or the scattering problem in lower order Sobolev class H4/3-δ1+δ∩H1+δ, where δ>0 is small.
AB - We consider the system of quadratic nonlinear Klein-Gordon equations in two space dimensions. Under the mass condition such that 2m1>m2, we construct the scattering operator in an almost natural weighted Sobolev class H1+δ,1 or the scattering problem in lower order Sobolev class H4/3-δ1+δ∩H1+δ, where δ>0 is small.
KW - Bilinear estimates
KW - Nonlinear Klein-Gordon equations
KW - Quadratic nonlinearity
KW - Two space dimensions
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U2 - 10.1016/j.jde.2013.01.035
DO - 10.1016/j.jde.2013.01.035
M3 - Article
AN - SCOPUS:84874278162
VL - 254
SP - 3615
EP - 3646
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 8
ER -