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

1999/10/07 by Jean Dolbeault, Gerhard Rein
Mathematics · Physics and Astronomy · #math.AP #math-ph #math.MP #msc:35B40 #msc:82C40

paper · pdf

published as Mathematical Models and Methods in Applied Sciences Vol. 11, No. 3, 407 - 432 (2001) · 34 pages, LaTeX

arxiv created 1999/10/07 · arxiv updated 2009/11/30

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 (Schrödinger-Poisson system, nonlinear Schrödinger equation).

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