论文标题
分布依赖的非线性SPDE，并应用于随机传输类型方程
Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations
论文作者
论文摘要
通过使用规律性近似参数，根据整个历史记录和在足够强的噪声下的分布而定为一类非线性SPDE的全局存在和唯一性。作为应用，全球存在和唯一性被证明是分配依赖的随机运输类型方程，这些方程是由随机流体力学产生的，其力取决于历史和环境。特别是，当噪声足够强时，带有或没有科里奥利效应的分布依赖性随机凸轮方程具有独特的全局解决方案，而对于确定性模型波破坏了。这表明噪声几乎可以防止爆炸。
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.
