On classical solutions of the Nordstr\"om-Vlasov system
Calogero, Simone ; Rein, Gerhard
arXiv, 0304021 / Harvested from arXiv
Text on arXiv
The Nordstr\"om-Vlasov system describes the dynamics of a self-gravitating ensemble of collisionless particles in the framework of the Nordstr\"om scalar theory of gravitation. We prove existence and uniqueness of classical solutions of the Cauchy problem in three dimensions and establish a condition which guarantees that the solution is global in time. Moreover, we show that if one changes the sign of the source term in the field equation, which heuristically corresponds to the case of a repulsive gravitational force, then solutions blow up in finite time for a large class of initial data. Finally, we prove global existence of classical solutions for the one dimensional version of the system with the correct sign in the field equation.
Publié le : 2003-04-14
Classification:  Mathematical Physics,  General Relativity and Quantum Cosmology,  Mathematics - Analysis of PDEs,  35Q75,35L99,83D05 
@article{0304021,
     author = {Calogero, Simone and Rein, Gerhard},
     title = {On classical solutions of the Nordstr\"om-Vlasov system},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0304021}
}

Calogero, Simone; Rein, Gerhard. On classical solutions of the Nordstr\"om-Vlasov system. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0304021/