Abstract ：Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this series of lectures, I will discuss the recent development in singularity formation of 3D Euler equations with smooth initial data and boundary using a combination of analysis and rigorous numerics. Time permitting, I will discuss the following topics.
 
(1)   Background of the problem, difficulties, and existing methods.
 
(2)   Dynamic rescaling reformulation of the 3D Euler equations and construction of the approximate self-similar blowup profile.
 
(3)   Sharp Holder estimates, weighted energy estimates, and L^infty based finite rank perturbation.
 
(4)   Rigorous numerics.  We will combine numeric methods from numeric PDE, numeric integrals, numeric analysis, and analytic ideas from induction, harmonic analysis, and energy estimates. All the computation can be implemented in parallel in a straightforward manner.
 
This series of lectures is based on joint works with Tom Hou.

Time&Venue:

2023-06-27  09:00-11:00  Room 1513, Sciences Building No.1

2023-06-28  09:00-1100  Room 1513, Sciences Building No.1

2023-06-30  09:00-11:00  Room 1513, Sciences Building No.1