Finite-time Singularity formation for Strong Solutions to the axi-symmetric $3D$ Euler Equations

26 Feb 2018 Elgindi Tarek M. Jeong In-Jee

For all $\epsilon>0$, we prove the existence of finite-energy strong solutions to the axi-symmetric $3D$ Euler equations on the domains $ \{(x,y,z)\in\mathbb{R}^3: (1+\epsilon|z|)^2\leq x^2+y^2\}$ which become singular in finite time. We further show that solutions with 0 swirl are necessarily globally regular... (read more)

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