Friday April 4th, 2025 | |
| Time: | 11:00 AM - 12:00 PM |
| Title: | Axisymmetry and vorticity blowup in compressible Euler equations |
| Speaker: | Jiajie Chen, NYU |
| Abstract: | |
| While it is known that a pre-shock or implosion singularity can form in finite time for the compressible Euler equations from smooth initial data, whether the vorticity blows up in finite time has remained an open problem. In this talk, we will explore the Euler equations with axisymmetry. Using (nearly) axisymmetric flow, we construct vorticity blowup 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, where the swirl velocity exhibits full stability as opposed to finite co-dimension stability. | |