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

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

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/math/9910041v1

Date

2001

Journal name

Mathematical Models and Methods in Applied Sciences

Volume

Number

Publisher

World Scientific

Pages

407-432

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 / Keywords

Scalings; Lyapunov functional; intermediate asymptotics; Strichartz estimate; dispersion; kinetic equations; Vlasov–Poisson system; Euler–Poisson system; fluid dynamics; Wigner equation; Schrödinger equation