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Global classical solutions to the 3D Nordström-Vlasov system. (English) Zbl 1123.35080
The article is concerned with the Cauchy problem for the Nordström-Vlasov system, presenting a Lorentz invariant kinetic model describing the evolution of self-gravitating collisionless matter under the assumption that the gravitational forces are mediated by a scalar field. The main result is an existence theorem of a unique global solution of this system in three dimensions for smooth initial data of the scalar field and smooth initial particle density with compact support.

MSC:
35Q75 PDEs in connection with relativity and gravitational theory
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
83C15 Exact solutions to problems in general relativity and gravitational theory
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