Chae, DonghoImanuvilov, Oleg Yu2018-11-152018-11-151998-10-15Chae, 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. 1-17.1072-6691https://hdl.handle.net/10877/7797We 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.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalEuler equationsAxisymmetryWeak solutionArticle