Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations
Abstract
By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole history and the distribution under strong enough noise. As applications, the global existence and uniqueness are proved for distribution-path dependent stochastic transport type equations, which are arising from stochastic fluid mechanics with forces depending on the history and the environment. In particular, the distribution-path dependent stochastic Camassa--Holm equation with or without Coriolis effect has a unique global solution when the noise is strong enough, whereas for the deterministic model wave-breaking may occur. This indicates that the noise may prevent blow-up almost surely.
Keywords
Cite
@article{arxiv.2007.09188,
title = {Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations},
author = {Panpan Ren and Hao Tang and Feng-Yu Wang},
journal= {arXiv preprint arXiv:2007.09188},
year = {2022}
}