Rough Stochastic Viscous Camassa-Holm equation

Source abstract

In this paper, we establish well-posedness results for the viscous Camassa--Holm equation driven by the additive Gaussian noise $(1-\partial_x^2)^{-η}ξ$, where $ξ$ denotes the space-time white noise and $η>-1/12$. This formulation includes spatially colored noise for $η>0$, space-time white noise for $η=0$, and rough noise for $-1/12 -1/12$. Furthermore, when $η>1/4$, we establish global well-posedness by deriving suitable energy estimates.