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arXiv · 2005.09374

Diffusion-approximation for a kinetic spray-like system with random forcing

Arnaud Debussche·Angelo Rosello·Julien Vovelle
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Abstract

We study a kinetic toy model for a spray of particles immersed in an ambient fluid, subject to some additional random forcing given by a mixing, space-dependent Markov process. Using the perturbed test function method, we derive the hydrodynamic limit of the kinetic system. The law of the limiting density satisfies a stochastic conservation equation in Stratonovich form, whose drift and diffusion coefficients are completely determined by the law of the stationary process associated with the Markovian perturbation.

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Arnaud Debussche, Angelo Rosello, Julien Vovelle. 2020-05-19. Diffusion-approximation for a kinetic spray-like system with random forcing. https://arxiv.org/abs/2005.09374

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