Speaker: In-Jee Jeong，Korea Institute for Advanced Study

Inviter: 薛志龙

Title: Instantaneous and continuous loss of regularity for the 3D Euler equations

Language: English

Time & Venue: 2026.10.14 09:00-10:00 思源楼S817

Abstract: In this talk, I will present a construction of solutions to the three-dimensional incompressible Euler equations whose vorticity loses Sobolev regularity instantaneously and continuously in time. For every (0<s<3/2), we construct arbitrarily small initial vorticity in (Hs(ℝ3)) and a corresponding solution whose exact Sobolev regularity at time (t) is ((s-ct)/(1+ct)), for some (c>0), on a short time interval. The solution remains classical locally in space and is unique in a suitable class. I will explain the mechanism behind this loss of regularity: a nearly steady background flow creates hyperbolic deformation that both stretches and generates finer scales in a high-frequency vorticity perturbation. Combining spatially separated copies of this construction yields the continuous decrease of the Sobolev exponent. This is joint work with Luis Martínez-Zoroa and Wojciech S. Ożański.