Existence of Axisymmetric Weak Solutions of the 3-D Euler Equations for Near-Vortex-Sheet Initial Data
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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.
CitationChae, D. & Imanuvilov, O. Y. (1998). Existence of Axisymmetric Weak Solutions of the 3-D Euler Equations for Near-Vortex-Sheet Initial Data, Electronic Journal of Differential Equations, 1998(26), pp. 1-17.
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