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Global existence, uniqueness and asymptotic behaviour of solutions of the Wigner-Poisson and Schrödinger-Poisson systems. (English) Zbl 0808.35116

Summary: We prove global existence and uniqueness of classical solutions of the Wigner-Poisson and Schrödinger-Poisson systems of equations for both repulsive and attractive potentials. In the repulsive case, we prove decay estimates for the particle density, the potential and the solutions.

MSC:

35Q40 PDEs in connection with quantum mechanics
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
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