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Problème de Cauchy pour des systèmes de Klein-Gordon-Schrödinger. (French) Zbl 0538.35016
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.

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
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