%0 Journal Article
%T Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data
%A Dongho Chae
%A Oleg Yu Imanuvilov
%J Electronic Journal of Differential Equations
%D 1998
%I Texas State University
%X 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.
%K Euler equations
%K axisymmetry
%K weak solution.
%U http://ejde.math.txstate.edu/Volumes/1998/26/abstr.html