A General Framework for Solving Singular SPDEs with Applications to Fluid Models Driven by Pseudo-differential Noise
Abstract
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.
Keywords
Cite
@article{arxiv.2208.08312,
title = {A General Framework for Solving Singular SPDEs with Applications to Fluid Models Driven by Pseudo-differential Noise},
author = {Hao Tang and Feng-Yu Wang},
journal= {arXiv preprint arXiv:2208.08312},
year = {2023}
}