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.

中文翻译：

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具有随机强迫的动力学喷雾状系统的扩散近似

我们研究了沉浸在环境流体中的粒子喷雾的动力学玩具模型，受到混合、空间相关马尔可夫过程给出的一些额外随机力的影响。使用扰动测试函数方法，我们推导出动力学系统的流体动力学极限。极限密度定律满足 Stratonovich 形式的随机守恒方程，其漂移和扩散系数完全由与马尔可夫扰动相关的平稳过程定律决定。