Solving Landau equation for some soft potentials through a probabilistic approach

• 成果类型: Article
• 署名作者: Guérin, H
• 署名单位: Universite Paris Nanterre
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1050689592
• 发表日期: 2003
• 页码: 515-539
• 关键词: fokker-planck equation; homogeneous boltzmann; Connection; EXISTENCE

摘要

This article deals with a way to solve the spatially homogeneous Landau equation using probabilistic tools. Thanks to the study of a nonlinear stochastic differential equation driven by a space-time white noise, we state the existence of a measure solution of the Landau equation with probability measure initial data, for a generalization of the Maxwellian molecules case. Then, by approximation of the Landau coefficients, the first result helps us to state the existence of a measure solution for some soft potentials [gamma is an element of (- 1, 0)]. This second part is based on the use of nonlinear stochastic differential equations and some martingale problems.