Stable self-similar blowup for a family of nonlocal transport equations

2019/06/13 by Elgindi, Tarek M., Ghoul, Tej-Eddine, Masmoudi, Nader · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1906.05811

Abstract

We consider a family of non-local 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.

Cited by

• Finite time blow-up analysis for the generalized Proudman-Johnson model
• Homogeneous steady states for the generalized surface quasi-geostrophic equations

Related

• Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data I: Analysis
• On the Stability of Self-similar Blow-up for C^1,α Solutions to the Incompressible Euler Equations on ℝ³
• Self-similar blow-up solutions of d-dimensional incompressible Euler equations with C^1,(1-2/d)- velocity
• Singular solutions with vorticity control for a nonlocal system of evolution equations
• Non-implosion mechanism of 3D incompessible Euler equations