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
Dolbeault, Jean; Rein, Gerhard (2001), 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, Mathematical Models and Methods in Applied Sciences, 11, 3, p. 407-432. http://dx.doi.org/10.1142/S021820250100091X
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/math/9910041v1
Journal nameMathematical Models and Methods in Applied Sciences
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Abstract (EN)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 behavior of the solutions and can be applied to other models in kinetic theory (two-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).
Subjects / KeywordsScalings; Lyapunov functional; intermediate asymptotics; Strichartz estimate; dispersion; kinetic equations; Vlasov–Poisson system; Euler–Poisson system; fluid dynamics; Wigner equation; Schrödinger equation
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