Mathematical Models and Methods in Applied Sciences F 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 F 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
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应用科学中的数学模型和方法 F Vlasov-poisson 和 Euler-poisson 系统以及运动方程、流体动力学和量子物理相关模型的时间相关重缩放和 Lyapunov 泛函
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通讯作者：
Gerhard Rein
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作者：
Jean Dolbeault;Gerhard Rein
我们研究了Vlasov-Poisson和Euler-Poisson系统的重标度变换，并在等离子体物理情况下导出了可用于分析色散效应的Lyapunov泛函。该方法还可用于研究解的长时间行为，并可应用于动力学（具有外磁场的二维对称Vlasov-Poisson系统），流体动力学（气体的欧拉系统）和量子物理（schrodinger - poisson系统，非线性schrodinger方程）中的其他模型。
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 eeects. 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 eld), in uid dynamics (Euler system for gases) and in quantum physics (Schrr odinger-Poisson system, nonlinear Schrr odinger equation).