Analysis and Applied Mathematics Seminar
Dallas Albritton
University of Wisconsin-Madison
Non-uniqueness and vanishing viscosity in the forced 2D Euler equations
Abstract: The forced 2D Euler equations exhibit non-unique solutions with vorticity in L^p, p > 1, whereas the corresponding Navier-Stokes solutions are unique. We investigate whether the inviscid limit from the forced 2D Navier-Stokes to Euler equations is a selection principle capable of "resolving" the non-uniqueness. We focus on solutions in a neighborhood of the non-uniqueness scenario discovered by Vishik; specifically, we incorporate viscosity and consider epsilon-size perturbations of his initial datum. We discover a uniqueness threshold below which the vanishing viscosity solution is unique and radial, and at which certain vanishing viscosity solutions converge to non-unique, non-radial solutions. Joint work with Maria Colombo and Giulia Mescolini (EPFL).
Monday February 2, 2026 at 4:00 PM in 636 SEO