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Instability of finite time blow-ups for incompressible Euler

Banff International Research Station for Mathematical Innovation and Discovery

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 explain why the prediction of such a blow-up, via direct numerical experiments, is so difficult. We will describe how, in such a scenario, the solution becomes unstable as time approaches the blow-up time. The method use 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. </p>

This work was partially supported by the NSFDMS-1907981. </p>

This a joint work with Misha Vishik and Laurent Lafleche.</p>

Mathematics; Partial differential equations; Fluid mechanics; Fluid dynamics

video/mp4

Author affiliation: University of Texas at Austin

2021-05-23

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/78411

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/