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

@inproceedings{Forstner2021SurfaceQE, title={Surface Quasi-Geostrophic Equation driven by Space-Time White Noise}, author={Philipp Forstner and Martin Saal}, year={2021} }

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…

## One Citation

### A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity

- Mathematics
- 2022

We study the surface quasi-geostrophic equation with an irregular spatial perturbation $$ \partial_{t }\theta+ u\cdot\nabla\theta = -\nu(-\Delta)^{\gamma/2}\theta+ \zeta,\qquad…

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