Uniqueness criteria for the Vlasov--Poisson system and applications to semiclassical analysis

Abstract

We review some uniqueness criteria for the Vlasov--Poisson system, emerging as corollaries of stability estimates in strong or weak topologies, and show how they serve as a guideline to solve problems arising in semiclassical analysis. Different topologies allow to treat different classes of quantum states.

arXiv comment14 pages

References in corpus (5)

• The Schrödinger Equation in the Mean-Field and Semiclassical Regime
• Propagation of Moments and Semiclassical Limit from Hartree to Vlasov Equation
• Global Semiclassical Limit from Hartree to Vlasov Equation for Concentrated Initial Data
• On the $L^2$ Rate of Convergence in the Limit from the Hartree to the Vlasov$\unicode{x2013}$Poisson Equation
• Optimal Semiclassical Regularity of Projection Operators and Strong Weyl Law