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

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

2008-03-12

arxiv.org/abs/0803.1784v1

Mathematics

Analysis of PDEs

11 pages

Scientific paper

10.1088/0951-7715/21/9/007

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.

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