SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 5090-5120, January 2020.
This paper deals with the combined incompressible quasineutral limit of the weak martingale solution of the compressible Navier--Stokes--Poisson system perturbed by a stochastic forcing term in the whole space. In the framework of ill-prepared initial data, we show the convergence in law to a weak martingale solution of a stochastic incompressible Navier--Stokes system. The result holds true for any arbitrary nonlinear forcing term with suitable growth. The proof is based on the analysis of acoustic waves but since we are dealing with a stochastic partial differential equation, the existing deterministic tools for treating this second-order equation break down. Although this might seem a minor modification, to handle the acoustic waves in the stochastic compressible Navier--Stokes system, we produce suitable dispersive estimate for a first-order system of equations, which are an added value to the existing theory. As a by-product of this dispersive estimate analysis, we are also able to prove a convergence result in the case of the zero-electron-mass limit for a stochastic fluid dynamical plasma model.

中文翻译：

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随机Navier-Stokes-Poisson系统的组合不可压缩拟中立极限

SIAM数学分析期刊，第52卷，第5期，第5090-5120页，2020年1月。
本文研究了在整个空间中受随机强迫项干扰的可压缩Navier-Stokes-Poisson系统的弱mar问题组合的不可压缩拟中性极限。在准备不充分的初始数据的框架中，我们证明了法律上收敛于随机不可压缩的Navier-Stokes系统的弱mar解决方案。对于具有适当增长量的任何任意非线性强迫项，该结果均成立。该证明基于对声波的分析，但是由于我们正在处理一个随机的偏微分方程，因此用于处理该二阶方程的现有确定性工具会崩溃。尽管这似乎是一个较小的修改，但要处理随机可压缩的Navier-Stokes系统中的声波，我们为一阶方程组产生合适的色散估计，这是现有理论的附加值。作为这种色散估计分析的副产品，我们还能够证明随机流体动力学等离子体模型在零电子质量极限的情况下的收敛结果。