DIFFUSION-APPROXIMATION FOR A KINETIC EQUATION WITH PERTURBED VELOCITY REDISTRIBUTION PROCESS

• 成果类型: Article
• 署名作者: Caillerie, Nils; Vovelle, Julien
• 署名单位: Georgetown University; Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1619
• 发表日期: 2021
• 页码: 1299-1335
• 关键词: nonlinear schrodinger-equation; models; limit; chemotaxis

摘要

We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the limit we obtain is a parabolic stochastic partial differential equation on the macroscopic parameter, the density here.