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Pré-Publication, Document De Travail Année : 2020

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

Résumé

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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Dates et versions

hal-02612572 , version 1 (19-05-2020)
hal-02612572 , version 2 (02-07-2020)

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Arnaud Debussche, Angelo Rosello, Julien Vovelle. Diffusion-approximation for a kinetic spray-like system with random forcing. 2020. ⟨hal-02612572v1⟩
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