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arXiv · 2007.09188

Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations

Panpan Ren·Hao Tang·Feng-Yu Wang
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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.

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Panpan Ren, Hao Tang, Feng-Yu Wang. 2020-07-17. Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations. https://arxiv.org/abs/2007.09188

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