| Abstract: |
| It remains an open problem whether the 3D incompressible Euler equations can develop finite-time singularity from smooth initial data in the whole space. In this talk, I will review some most recent results on finite-time blowups mostly with self-similar features, divided into two parts. In the first part, I will talk about traditional self-similar finite-time blowup and the dynamic rescaling method for establishing asymptotically self-similar finite-time blowup. In the second part, I will talk about recent findings on potential self-similar finite-time blowups of the 3D Euler equations with multi-scale features, which are closely related to traveling wave solutions and provide a new approach towards Euler singularity. |
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