The Surface Quasi-Geostrophic Equation with Random Diffusion

TL;DR

This paper proves that the surface quasi-geostrophic equation with random diffusion has a unique, globally existing solution with high probability, under certain regularity conditions, extending previous work in the field.

Contribution

It establishes global existence and uniqueness results for the surface quasi-geostrophic equation with stochastic diffusion, a novel extension with probabilistic analysis.

Findings

Global existence and uniqueness with high probability

Solutions satisfy a Gevrey type regularity bound

Builds on recent deterministic and stochastic PDE research

Abstract

Consider the surface quasi-geostrophic equation with random diffusion, white in time. We show global existence and uniqueness in high probability for the associated Cauchy problem satisfying a Gevrey type bound. This article is inspired by recent work of Glatt-Holtz and Vicol.