Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$

TL;DR

This paper investigates stochastic quasi-geostrophic equations with fractional dissipation on Euclidean space, establishing existence of solutions and pathwise uniqueness in 2D sub-critical cases, advancing understanding of their mathematical properties.

Contribution

It proves existence of martingale solutions and pathwise uniqueness for stochastic fractional quasi-geostrophic equations, which was previously unestablished in this setting.

Findings

Existence of martingale solutions for the equations.

Pathwise uniqueness in 2D sub-critical case.

Extension of mathematical understanding of stochastic quasi-geostrophic models.

Abstract

Stochastic fractionally dissipative quasi-geostrophic type equation on $R^d$ with a multiplicative Gaussian noise is considered. We prove the existence of a martingale solution. In the 2D sub-critical case we prove also the pathwise uniqueness of the solutions.