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##### Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number

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### Remarks on the blow-up criterion of the 3D incompressible Euler equations

Dr. Dongho Chae

Mathematics at Sungkyunkwan University

Abstract:   In this talk we present a study of finite time blow-up criterion of classical solutions of the 3-D homogeneous incompressible Euler equations. We find it is controlled by the Besov space, $\dot{B}^0_{\infty, 1}$, norm of the it two components of the vorticity. For the axisymmetric flows with swirl we deduce that the blow-up of solution is controlled by the same Besov space norm of the angular component of the vorticity.

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