Vol. 14, No. 3, 2021

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Stable self-similar blow-up for a family of nonlocal transport equations

Tarek M. Elgindi, Tej-eddine Ghoul and Nader Masmoudi

Vol. 14 (2021), No. 3, 891–908
Abstract

We consider a family of nonlocal problems that model the effects of transport and vortex stretching in the incompressible Euler equations. Using modulation techniques, we establish stable self-similar blow-up near a family of known self-similar blow-up solutions.

Keywords
singularity, Euler equation, 1-dimensional models
Mathematical Subject Classification 2010
Primary: 35Q31, 35Q35
Milestones
Received: 13 June 2019
Revised: 7 October 2019
Accepted: 21 November 2019
Published: 18 May 2021
Authors
Tarek M. Elgindi
UC San Diego
La Jolla, CA
United States
Tej-eddine Ghoul
New York University Abu Dhabi
Abu Dhabi
United Arab Emirates
Nader Masmoudi
New York University Abu Dhabi
Abu Dhabi
United Arab Emirates