Global existence of classical solutions for a Vlasov-Schrodinger-Poisson system

@article{Abdallah2006GlobalEO,
  title={Global existence of classical solutions for a Vlasov-Schrodinger-Poisson system},
  author={N. B. Abdallah and F. M{\'e}hats and G. Quinio},
  journal={Indiana University Mathematics Journal},
  year={2006},
  volume={55},
  pages={1423-1448}
}
Global existence and uniqueness of a classical solution of the two dimensional Vlasov equation coupled to the Schrodinger-Poisson system is proven. The two dimensional driving forces appearing in the Vlasov equation are deduced from the electrostatic potential in the Born-Oppenheimer approximation and take into account the quantum behaviour in the third direction. The electrostatic potential is computed by solving a three dimensional Poisson equation. The existence and uniqueness of the… Expand
6 Citations

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