TY - JOUR
T1 - A bilinear estimate and its application to a quadratic nonlinear Klein-Gordon equation in two space dimensions
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
N1 - Funding Information:
N.H. would like to thank Professor Naohito Tomita for fruitful discussions on his paper [14] and the estimates of bilinear operators. The work of N.H. is partially supported by KAKENHI (No. 19340030 ) and the work of P.I.N. is partially supported by CONACYT (No. 166579 ) and PAPIIT IN100616 .
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/3/15
Y1 - 2016/3/15
N2 - We study the existence of the wave operators for the nonlinear Klein-Gordon equation with quadratic nonlinearity in two space dimensions u=λu2, (t,x)∈R×R2. We prove existence of wave operators in lower order Sobolev spaces by using estimates of bilinear operators associated with Klein-Gordon equation.
AB - We study the existence of the wave operators for the nonlinear Klein-Gordon equation with quadratic nonlinearity in two space dimensions u=λu2, (t,x)∈R×R2. We prove existence of wave operators in lower order Sobolev spaces by using estimates of bilinear operators associated with Klein-Gordon equation.
KW - Bilinear estimates
KW - Nonlinear Klein-Gordon equations
KW - Quadratic nonlinearity
KW - Two space dimensions
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U2 - 10.1016/j.jfa.2016.01.016
DO - 10.1016/j.jfa.2016.01.016
M3 - Article
AN - SCOPUS:84958102238
SN - 0022-1236
VL - 270
SP - 1971
EP - 1994
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 6
ER -