In this talk, we will discuss the interaction between the stability, and the propagation of regularity, for solutions to the incompressible 3D Euler equation. It is still unknown whether a solution with smooth initial data can develop a singularity in finite time. We will describe how, in such a scenario, the solution becomes unstable as time approaches the blow-up time. It explains why it is so difficult to obtain numerical evidence of such blow-up. The method uses the relation between the vorticity of the solution, and the bi-characteristic amplitude solutions, which describe the evolution of the linearized Euler equation at high frequency. In the axisymmetric case, we can also study the instability of blow-up profiles.
This work was partially supported by the NSFDMS-1907981. This is a joint work with Misha Vishik and Laurent Lafleche.
Please find below the zoom link and the Abstract of the talk. Do not hesitate to let me know if there are any difficulties.
Meeting Number (access code): 898 1269 9925
Meeting Password: 492381
More about Alexis Vasseur’s scientific achievements: https://web.ma.utexas.edu/users/vasseur/.