On the lifespan of axisymmetric incompressible Euler equations with a small initial swirl: On the lifespan of axisymmetric incompressible Euler equations
Authors: 
Zijin Li, Taoran ZhouAuthors Info & Claims
Abstract
We show the lifespan of a strong solution to the incompressible 3D axially symmetric Euler system in can be arbitrarily large if the initial swirl is small enough. A precise lower bound of the lifespan, depending on the size of , 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.
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© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
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Birkhauser Verlag
Switzerland
Publication History
Published: 02 November 2024
Accepted: 11 October 2024
Revision received: 09 October 2024
Received: 30 May 2024
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