Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data
Electronic journal of differential equations, Tome 1998 (1998)
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.
@article{EJDE_1998__1998__a0,
author = {Chae, Dongho and Imanuvilov, Oleg Yu.},
title = {Existence of axisymmetric weak solutions of the {3-D} {Euler} equations for near-vortex-sheet initial data},
journal = {Electronic journal of differential equations},
year = {1998},
volume = {1998},
zbl = {0903.35050},
language = {en},
url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a0/}
}
TY - JOUR AU - Chae, Dongho AU - Imanuvilov, Oleg Yu. TI - Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data JO - Electronic journal of differential equations PY - 1998 VL - 1998 UR - http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a0/ LA - en ID - EJDE_1998__1998__a0 ER -
%0 Journal Article %A Chae, Dongho %A Imanuvilov, Oleg Yu. %T Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data %J Electronic journal of differential equations %D 1998 %V 1998 %U http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a0/ %G en %F EJDE_1998__1998__a0
Chae, Dongho; Imanuvilov, Oleg Yu. Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data. Electronic journal of differential equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a0/