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Finite-time Singularity Formation for Strong Solutions to the Euler equations, II
Tarek M. Elgindi, In-Jee Jeong
This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric Euler equation in the domains $\{(x_1,x_2,…
Finite-time Singularity Formation for Strong Solutions to the Euler Equations, I
Tarek M. Elgindi, In-Jee Jeong
In this paper and the companion paper [EJE2], we establish finite-time singularity formation for finite-energy strong solutions to the axi-symmetric Euler equations in the dom…
Finite-time Singularity Formation for Strong Solutions to the Boussinesq System
Tarek M. Elgindi, In-Jee Jeong
The global regularity problem for the Boussinesq system is a well known open problem in mathematical fluid dynamics. As a follow up to our work \cite{EJSI}, we give examples of fin…
Self-similar solutions for dyadic models of the Euler equations
In-Jee Jeong
We show existence of self-similar solutions satisfying Kolmogorov's scaling for generalized dyadic models of the Euler equations, extending a result of Barbato, Flandoli, and Moran…
On the Effects of Advection and Vortex Stretching
Tarek M. Elgindi, In-Jee Jeong
We prove finite-time singularity formation for De Gregorio's model of the three-dimensional vorticity equation in the class of vorticities for some …