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arXiv · 1707.07874

Diffusion-approximation in stochastically forced kinetic equations

Arnaud Debussche·Julien Vovelle
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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.

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Arnaud Debussche, Julien Vovelle. 2017-07-25. Diffusion-approximation in stochastically forced kinetic equations. https://arxiv.org/abs/1707.07874

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