Applied Math And Analysis Seminar

Some recent progress on singularity formation in incompressible fluids and related models

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Speaker(s): Jiajie Chen
Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In 2014, Hou-Luo obtained strong numerical evidence that the 3D asymmetric Euler equations with a boundary can develop a potential finite-time singularity. In this talk, we will introduce a framework to study the potential singularity in the Hou-Luo scenario with smooth data and discuss the difficulties and some results toward a rigorous proof. In the case without a boundary, the effect of the advection is one of the obstacles to singularity formation. In a model problem (De Gregorio model), we will briefly show that the advection can prevent blowup if the strength of advection is strong enough.

Physics 119