  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.

Analysis of PDEs;Probability