Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective
Analysis of PDEs
2020-12-16 v2 Mathematical Physics
math.MP
Abstract
Solutions to a singular one-dimensional Vlasov equation are obtained as the semiclassical limit of the Wigner transform associated to a logarithmic Schrodinger equation. Two frameworks are considered, regarding in particular the initial position density: Gaussian initial density, or smooth initial density away from vacuum. For Gaussian initial densities, the analysis also yields global solutions to the isothermal Euler system that do not enter the frame of regular solutions to hyperbolic systems by P. D. Lax.
Keywords
Cite
@article{arxiv.1506.07339,
title = {Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective},
author = {Rémi Carles and Anne Nouri},
journal= {arXiv preprint arXiv:1506.07339},
year = {2020}
}
Comments
16 pages. A new result has been incorporated and the paper has been reorganized