| Abstract: |
| We consider a general class of non-diffusive active scalar equations with constitutive laws obtained via an operator T that is singular of order r0∈[0,2]. We obtain ill/well-posedness results for various values for r0. 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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