Quasigeostrophic equation with random initial data in negative-order Sobolev space

Abstract

This paper is concerned with the Cauchy problem of the Quasigeostrophic equation on the torus $${\mathbb {T}}^2$$ . We prove the almost sure existence and uniqueness of the global solution with the random initial data in $${\mathcal {H}}^s({\mathbb {T}}^2), s\in [-1,0)$$ .