| Abstract: |
| In this talk, we will show the non-uniqueness of weak solutions to 3D MHD equations, where the viscosity and resistivity can be larger than the Lions exponent. The non-uniqueness is sharp near one endpoint of the Lady\v{z}enskaja-Prodi-Serrin condition. Moreover, the constructed weak solutions admit the partial regularity outside a small fractal singular set in time with small Hausdorff dimension. At last, we will also present the non-uniqueness of probabilistic strong and analytic weak solutions in the stochastic setting. |
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