## Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data

### Summary

Summary: We study the initial value problem for the 3-D Euler equation when the fluid is inviscid and incompressible, and flows with axisymmetry and without swirl. On the initial vorticity $\omega_0$, we assumed that $\omega_0/r$ belongs to $L(\log L (\Bbb R^3))^{\alpha}$ with $\alpha$, where $r$ is the distance to an axis of symmetry. To prove the existence of weak global solutions, we prove first a new a priori estimate for the solution.

35Q35, 76C05

### Keywords/Phrases

Euler equations, axisymmetry, weak solution