| Abstract: |
| With Andrea Nahmod, Natasa Pavlovic, and Gigliola Staffilani, we consider some results in constructing extremely low regularity flows for the inviscid surface quasi-geostrophic equation (SQG) in the periodic setting. Our first result is the construction of solutions globally in time almost surely for a family of modified SQG equations by constructing an invariant Gibbs measure and extracting a solution by Galerkin approximation; our method here requires some positive amount of smoothing and so does not include the inviscid case. To understand whether such smoothing is necessary or an artifact of our method, we will therefore also present results toward constructing global solutions to a variation of SQG with stochastic forcing using the theory of controlled solutions developed by M. Gubinelli and M. Jara. |
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