Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson and Euler-Poisson systems, and for related models of kinetic equations, fluid dynamics and quantum physics
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
We investigate rescaling transformations for the Vlasov-Poisson and Euler-Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion effects. The method is also used for studying the long time behaviour of the solutions and can be applied to other models in kinetic theory (2-dimensional symmetric Vlasov-Poisson system with an external magnetic field), in fluid dynamics (Euler system for gases) and in quantum physics (Schr\"odinger-Poisson system, nonlinear Schr\"odinger equation).
Keywords
Cite
@article{arxiv.math/9910041,
title = {Time-dependent rescalings and Lyapunov functionals for the Vlasov-Poisson and Euler-Poisson systems, and for related models of kinetic equations, fluid dynamics and quantum physics},
author = {Jean Dolbeault and Gerhard Rein},
journal= {arXiv preprint arXiv:math/9910041},
year = {2007}
}
Comments
34 pages, LaTeX