On the blow-up problem for the axisymmetric 3D Euler equations

Abstract

In this paper we study the finite time blow-up problem for the axisymmetric 3D incompressible Euler equations with swirl. The evolution equations for the deformation tensor and the vorticity are reduced considerably in this case. Under the assumption of local minima for the pressure on the axis of symmetry with respect to the radial variations we show that the solution blows-up in finite time. If we further assume that the second radial derivative vanishes on the axis, then system reduces to the form of Constantin-Lax-Majda equations, and can be integrated explicitly.

11 pages

References in corpus (1)

• Global Existence and Uniqueness of Weak Solutions of 3-D Euler Equations with Helical Symmetry in the Absence of Vorticity Stretching

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