Remarks on the blow-up criterion of the 3D Euler equations
نویسنده
چکیده
In this note we prove that the finite time blow-up of classical solutions of the 3-D homogeneous incompressible Euler equations is controlled by the Besov space, Ḃ0 ∞,1, norm of the 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. For the proof of these results we use the Beale-Kato-Majda criterion, and the special structure of the vortex stretching term in the vorticity formulation of the Euler equation.
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