Bachelot, Alain Problème de Cauchy pour des systèmes de Klein-Gordon-Schrödinger. (French) Zbl 0538.35016 C. R. Acad. Sci., Paris, Sér. I 296, 525-528 (1983). We investigate systems of Schrödinger and Klein-Gordon equations having quadratic non-linearities generalizing the Yukawa interaction. We resolve the global Cauchy problem using the \(L^{4/3}-L^ 4\) estimates for the propagator of the Schrödinger and Klein-Gordon equations. Cited in 1 Document MSC: 35G25 Initial value problems for nonlinear higher-order PDEs 35J10 Schrödinger operator, Schrödinger equation 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:Schrödinger equation; Klein-Gordon equation; quadratic non-linearities; Yukawa interaction; global Cauchy problem × Cite Format Result Cite Review PDF