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Problème de Cauchy global pour des systèmes de Dirac-Klein-Gordon. (Global Cauchy problem for Dirac-Klein-Gordon systems). (French) Zbl 0672.35071
Summary: We consider a massive Dirac system quadratically coupled with a wave equation in three space dimensions. The global Cauchy problem is well posed if the nonlinearities satisfy some algebraic conditions related to the Lorentz-invariance, the null condition and the compatibility of a sesquilinear form with the Dirac system. The fundamental example is the pseudoscalar Yukawa model of nuclear forces. We use some L 2 -L estimates in Sobolev spaces associated with the Lorentz metric, for the Dirac equation with a potential. We establish the completeness of the scattering operator for an electron in a free electromagnetic field.
35Q99PDE of mathematical physics and other areas
81Q05Closed and approximate solutions to quantum-mechanical equations
35G25Initial value problems for nonlinear higher-order PDE
35A05General existence and uniqueness theorems (PDE) (MSC2000)
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems