On the lifespan of axisymmetric incompressible Euler equations with a small initial swirl.

We show the lifespan of a strong solution to the incompressible 3D axially symmetric Euler system in R 3 can be arbitrarily large if the initial swirl is small enough. A precise lower bound of the lifespan, depending on the size of ‖ ∇ × (v 0 , θ e θ) ‖ L ∞ , is given. This extends the conclusion of Danchin (Proc Am Math Soc 141:1979–1993, 2012), in which the domain must be distant from the axis of symmetry. This may help us to have a better understanding of the nonlinear framework and the blowup mechanism inherent in the 3D axisymmetric Euler equations. [ABSTRACT FROM AUTHOR]