Scale-Invariant Incompressible Euler: Attractors, singularity formation, and hints of Lp non-uniqueness

Speaker: Ryan Murray, Associate Professor, North Carolina State University

Inviter: 秦国林 博士

Title: Scale-Invariant Incompressible Euler: Attractors, singularity formation, and hints of Lp non-uniqueness

Language: English

Time & Venue: 2026.08.21   15:30-16:30    南楼N613

Abstract: This talk will discuss a special class of scale-invariant solutions to the 2D Euler equation. Scale-invariant solutions describe the motion of certain classes of singularities of the Euler equations, and can be seen as one attempt to model certain coherent vortex structures. These solutions obey a non-linear scalar equation on the circle first identified by Elgindi and Jeong, and such solutions have local well-posedness for vorticities in Lp. Our results 1) give a characterization of the attractors of this system for bounded vorticities, and 2) demonstrate finite-time blowup for specific data in Lp. The talk will also discuss work which constructs analytic extensions of such solutions which have vorticity belonging to Lp(R^2), and which offer potential avenues for constructing non-unique solutions. This is joint work with Tarek Elgindi and Ayman Rimah Said.