Diffusion-approximation in stochastically forced kinetic equations
Analysis of PDEs
2020-03-23 v5 Probability
Abstract
We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and short-range correlation. In the scales and the regime we consider, the hydrodynamic equation is a scalar second-order stochastic partial differential equation. Compared to the deterministic case, we also observe a phenomenon of enhanced diffusion.
Cite
@article{arxiv.1707.07874,
title = {Diffusion-approximation in stochastically forced kinetic equations},
author = {Arnaud Debussche and Julien Vovelle},
journal= {arXiv preprint arXiv:1707.07874},
year = {2020}
}