论文标题
随机Navier-Stokes-Poisson系统的合并不可压缩的准化限制
The combined incompressible quasineutral limit of the stochastic Navier-Stokes-Poisson system
论文作者
论文摘要
本文介绍了可压缩的Navier-Stokes-poisson系统的弱曲构溶液的合并不可压缩的准次限极限，该系统在整个空间中被随机强迫术语扰动。在制备不足的初始数据的框架内，我们显示了法律上与随机不可压缩的Navier-Stokes系统的弱的Martingale解决方案的收敛。结果对于任何任意非线性强迫术语都具有适当的增长。证明基于对声波的分析，但是由于我们正在处理随机部分微分方程，这是用于处理此二阶方程分解的现有确定性工具。尽管这似乎是一个较小的修改，但要处理随机压缩的Navier-Stokes系统中的声波，我们为方程式的一阶系统提供了合适的分散估计，这是现有理论的附加值。作为该分散估计分析的副产品，在随机流体动力学等离子体模型的零电子质量极限的情况下，我们还能够证明会收敛结果。
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 breakdown. Although this might seem as a minor modification, to handle the acoustic waves in the stochastic compressible Navier-Stokes system, we produce suitable dispersive estimate for 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.
