Geodesic
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).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35Q35, 76C05
Keywords: Euler equations, axisymmetry, weak 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},
     publisher = {mathdoc},
     volume = {1998},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a0/}
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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/