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

Florian Bechtold; Theresa Lange; Jörn Wichmann

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arXiv · 2311.00670

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

Florian Bechtold·Theresa Lange·Jörn Wichmann

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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 $W$.

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Florian Bechtold, Theresa Lange, Jörn Wichmann. 2023-11-01. On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise. https://arxiv.org/abs/2311.00670

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