Type: Article

A bilinear estimate and its application to a quadratic nonlinear Klein-Gordon equation in two space dimensions

Hayashi, Nakao; Naumkin, Pavel I.;

Abstract:

Abstract We study the existence of the wave operators for the nonlinear Klein-Gordon equation with quadratic nonlinearity in two space dimensions (partial derivative(2)(t) - Delta + 1)u = lambda u(2), (t, x) is an element of R x R-2. We prove existence of wave operators in lower order Sobolev spaces by using estimates of bilinear operators associated with Klein-Gordon equation