Global existence of classical solutions for a Vlasov-Schrodinger-Poisson system Naoufel AbdallahFlorian MehatsGeraldine Quinio 82C4082C1035Q4082D3735P99quantum-classical couplingSchr\"odinger-PoissonVlasov-PoissonBorn-Oppenheimer approximationconvex minimizationtransport in nanostructures Global existence and uniqueness of a classical solution of the two dimensional Vlasov equation coupled to the Schr\"odinger-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 solution is proven by a fixed point argument on the Vlasov equation. It relies on the use of an a priori energy estimate, and on the resolution of the Schr\"odinger-Poisson system by convex minimization. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2659 10.1512/iumj.2006.55.2659 en Indiana Univ. Math. J. 55 (2006) 1423 - 1448 state-of-the-art mathematics http://iumj.org/access/