On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise

2023/11/01 by Florian Bechtold, Bechtold, Florian, Theresa Lange +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2311.00670

openalex publication_date 2023/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We study the surface quasi-geostrophic equation driven by a generic additive noise process W. By means of convex integration techniques, we establish existence of weak solutions whenever the stochastic convolution z associated with W is well defined and fulfills certain regularity constraints. Quintessentially, we show that the so constructed solutions to the non-linear equation are controlled by z in a linear fashion. This allows us to deduce further properties of the so constructed solutions, without relying on structural probabilistic properties such as Gaussianity, Markovianity or a martingale property of the underlying noise W.

Related

• Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise
• Surface Quasi-Geostrophic Equation driven by Space-Time White Noise
• Non-uniqueness in law of the two-dimensional surface quasi-geostrophic equations forced by random noise
• Surface quasi-geostrophic equations forced by random noise: prescribed energy and non-unique Markov selections
• Non-uniqueness in law of the surface quasi-geostrophic equations: the case of linear multiplicative noise