| Abstract: |
| We consider incompressible Euler flows with axisymmetry and without swirl. In $\mathbb{R}^{3}$, we prove the $t^{4/3}$-upper bound for the growth of the vorticity maximum. This was conjectured by Childress (Phys. D, 2008) and supported by numerical computations from Childress--Gilbert--Valiant (J. Fluid Mech., 2016). The key idea is to estimate the velocity maximum by the kinetic energy and conserved quantities related to the vorticity. This is a joint work with In-Jee Jeong (SNU). |
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