A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity

Martina Hofmanova, Rongchan Zhu, Xiangchan Zhu

We study the surface quasi-geostrophic equation with an irregular spatial perturbation $${\partial }_t\theta +u\cdot \nabla \theta =-\nu (-\Delta {)}^{\gamma /2}\theta +\zeta ,u={\nabla }^{\perp }(-\Delta {)}^{-1}\theta ,$$ on $…