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Nonuniqueness of solutions to the Euler equations with integrable vorticity

Anuj Kumar, Department of Mathematics, Berkeley
Speaker
Anuj Kumar, Department of Mathematics, Berkeley
When Oct 08, 2024
from 04:00 PM to 05:00 PM
Where Via zoom
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COLLOQUIUM TALK

Title: Nonuniqueness of solutions to the Euler equations with integrable vorticity

Abstract: Yudovich established the well-posedness of the two-dimensional incompressible Euler equations for solutions with bounded vorticity. DiPerna and Majda proved the existence of weak solutions with vorticity in L^p ( p > 1).  A celebrated open question is whether the uniqueness result can be generalized to solutions with L^p vorticity. In this talk, we resolve this question in negative for some p > 1. To prove nonuniqueness, we devise a new convex integration scheme that employs non-periodic, spatially-anisotropic perturbations, an idea that was inspired by our recent work on the transport equation. To construct the perturbation, we introduce a new family of building blocks based on the Lamb-Chaplygin dipole. This is a joint work with Elia Bruè and Maria Colombo.

Speaker Bio: Anuj Kumar is a Morrey Visiting Assistant Professor in the Department of Mathematics at the University of California, Berkeley. He completed his Ph.D. in Applied Mathematics at the University of California, Santa Cruz. His research interests lie in turbulent flows, variational methods, analysis of partial differential equations, and computational techniques.

Join Zoom Meeting
https://zoom.us/j/99700750177?pwd=bNROkLxXaSJ2bPX4prA5uRHXDBBR63.1

Meeting ID: 997 0075 0177
Passcode: 666777



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