Mathematics – Analysis of PDEs
Scientific paper
1999-10-07
Mathematical Models and Methods in Applied Sciences Vol. 11, No. 3, 407 - 432 (2001)
Mathematics
Analysis of PDEs
34 pages, LaTeX
Scientific paper
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).
Dolbeault Jean
Rein Gerhard
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