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

Lange Theresa, Scuola Normale Superiore di Pisa

This talk shall be concerned with 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 fulfils 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. This is joint work with Florian Bechtold (University of Bielefeld) and Jörn Wichmann (Monash University) (cf. arXiv preprint arXiv:2311.00670).

Area: CS11 - Stochastic Geophysical Fluid Dynamics (Antonio Agresti and Giulia Carigi)

Keywords: Surface quasi-geostrophic equation, convex integration, additive noise

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