Presented By: Differential Equations Seminar - Department of Mathematics
DE Seminar: Singularity Formation in Fluids
Jiajie Chen (Courant Institute, NYU)
Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, I will discuss singularity formation in incompressible Euler equations with smooth data and boundary and present a framework for stable nearly self-similar blowup. In contrast to incompressible fluids, singularity formation in compressible Euler equations has been established for a long time. However, whether vorticity blows up in compressible fluids at the first singular time remains an open problem. We will generalize several methods and insights from incompressible fluids to establish vorticity blowup in compressible Euler equations with smooth and non-vacuous initial data.
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