| Abstract: |
| We consider a general class of non-diffusive active scalar equations with constitutive laws obtained via an operator $\mathcal{T}$ that is singular of order $r_0\in[0, 2]$. We obtain ill/well-posedness results for various values for $r_0$. We then apply the results to several physical problems including the magnetogeostrophic equation, the incompressible porous media equation and the singular incompressible porous media equation. This is a joint work with Susan Friedlander and Fei Wang. |
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