Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 26, pp. 1-17.

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

Authors: Dongho Chae (Seoul National Univ., Korea)
         Oleg Yu Imanuvilov (Korea Inst. for Advanced Study)

Abstract: 
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 
$\alpha >1/2$, 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.  


Submitted October 9, 1998. Published October 15, 1998.  
Math Subject Classification: 35Q35, 76C05.
Key Words: Euler equations; axisymmetry; weak solution.