| Abstract: |
| The surface quasi-geostrophic (SQG) equation on $\mathbb{R}^2$ was shown in the late `00s to be well posed with smooth solutions. Recently, Constantin and Ignatova proposed a model for SQG on bounded open subsets of $\mathbb{R}^2$, defined in terms of the Dirichlet Laplacian. This model is particularly complex because it involves a nonlocal operator on a bounded domain. We will discuss this model, including physical motivation, existence, and regularity. |
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