Surface Quasi-Geostrophic Equation driven by Space-Time White Noise

2021/11/08 by Philipp Forstner, Forstner, Philipp, Martin Saal +1
Computer Science · Mathematics · #35Q86 #60H17 #60L30 #86A05 #86A10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Primary: 60H15 #Probability (math.PR) #Secondary: 35A01

paper · pdf · doi:10.48550/arxiv.2111.04644

openalex publication_date 2021/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Surface Quasi-Geostrophic equation (SQG) driven by space-time white noise and show the existence of a local in time solution by applying the theory of regularity structures. A main difficulty is the presence of Riesz-transforms in the non-linearity. We show how to lift singular integral operators with a particular structure to the level of regularity structures and using this result we deduce the existence of a solution to SQG by a renormalisation procedure. The fact that the Riesz-transforms act only in the spatial variable makes it necessary to use inhomogeneous models instead of the standard ones.

Citations

• An analytic BPHZ theorem for regularity structures

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