Electron. J. Diff. Eqns.,
Vol. 1998(1998), No. 26, pp. 1-17.
### Existence of axisymmetric weak solutions of the 3-D Euler equations
for near-vortex-sheet initial data

Dongho Chae & Oleg Yu Imanuvilov

**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
,
we assumed that
belongs to
with
, where
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.

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Dongho Chae
Department of Mathematics, Seoul National University
Seoul 151-742, Korea
e-mail: dhchae@math.snu.ac.kr |

Oleg Yu Imanuvilov
Korean Institute for Advanced Study
207-43 Chungryangri-dong Dongdaemoon-ku, Seoul, Korea
e-mail: oleg@kias.kaist.ac.kr |

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