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.