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

@article{Debussche2020DiffusionapproximationFA,
  title={Diffusion-approximation for a kinetic spray-like system with random forcing},
  author={Arnaud Debussche and Angelo Rosello and Julien Vovelle},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}
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… Expand
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