论文标题
一个通用框架，用于解决由伪差异噪声驱动的流体模型的奇异SPDES
A General Framework for Solving Singular SPDEs with Applications to Fluid Models Driven by Pseudo-differential Noise
论文作者
论文摘要
在本文中，我们关注的是在漂移和噪声系数中都包含奇异性的非线性SPDE，为此，Gelfand-Triple参数为（局部）单调SPDES原来是无效的。我们提出了一个\ emph {适当正则化}的一般框架，以解决这种单数SPDE。随着应用，（本地和全球）存在是针对由伪差异序列驱动的广泛的流体模型提出的，其中包括随机磁性水力动力学（因此，Navier-Stokes/Euler）方程，随机的Camassa-Holm类型方程，随机的camassa-holm类型方程，随机聚集了式式式，并进行了方程式和Storequest Quastic quasict quasict quasict quisict quasict quasict quisictict quisii- quisii- ii ii尼姆。因此，文献中得出的一些最新结果以统一的方式大大扩展。
In this paper we focus on nonlinear SPDEs with singularities included in both drift and noise coefficients, for which the Gelfand-triple argument developed for (local) monotone SPDEs turns out to be invalid. We propose a general framework of \emph{proper regularization} to solve such singular SPDEs. As applications, the (local and global) existence is presented for a broad class of fluid models driven by pseudo-differential noise of arbitrary order, which include the stochastic magnetohydrodynamics (hence Navier-Stokes/Euler) equations, stochastic Camassa-Holm type equations, stochastic aggregation-diffusion equation and stochastic surface quasi-geostrophic equation. Thus, some recent results derived in the literature are considerably extended in a unified way.
