Existence of Axisymmetric Weak Solutions of the 3-D Euler Equations for Near-Vortex-Sheet Initial Data
Date
1998-10-15
Authors
Chae, Dongho
Imanuvilov, Oleg Yu
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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 ω0, we assumed that ω0/r belongs to L(log L(ℝ3)) ɑ with ɑ > 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.
Description
Keywords
Euler equations, Axisymmetry, Weak solution
Citation
Chae, D. & Imanuvilov, O. Y. (1998). Existence of Axisymmetric Weak Solutions of the 3-D Euler Equations for Near-Vortex-Sheet Initial Data, <i>Electronic Journal of Differential Equations, 1998</i>(26), pp. 1-17.
Rights
Attribution 4.0 International