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

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 axisymmetric Euler equations with a boundary can develop a potential finite-time singularity from smooth initial data. In this talk, we will discuss some recent progress on the Hou-Luo blowup scenario and related models.