中科院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

调和分析和偏微分方程研讨班

报告人：Jiajie Chen（New york Univeristy ）

题  目：Axisymmetry and vorticity blowup

时  间：2024.07.16（星期二）16:00-17:00

地  点：S713

摘  要: While it is known that a pre-shock singularity or an implosion singularity for compressible Euler equations can form in finite time from smooth initial data, it is an outstanding open problem to determine whether the vorticity blows up or not.  In this talk, we will provide the first proof of finite-time blowup for the vorticity in the compressible Euler equations with smooth, localized, and non-vacuous initial data. The vorticity blowup occurs at the time of the first singularity and is accompanied by an axisymmetric implosion in which the swirl velocity enjoys full stability, as opposed to finite co-dimension stability.