报告题目：Axisymmetry and Vorticity Blowup

报 告 人：陈嘉杰 博士

报告人所在单位：Courant Institute, NYU

报告日期：2024-08-14

报告时间：9:30-10:30

报告地点：光华东主楼2201

报告摘要：

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 in R^d, with any d >= 2, from smooth, localized, and non-vacuous initial data. At the time of the first singularity, both vorticity blowup and implosion occur on a sphere S^{d-2}. Additionally, the solution exhibits a non-radial implosion, accompanied by a stable swirl velocity that is sufficiently strong to initially dominate the non-radial components and to generate the vorticity blowup.