Confinement of vorticity for the 2D Euler-alpha equations

David Ambrose; Milton Lopes Filho; Helena Nussenzveig Lopes

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arXiv · 1802.10161

Confinement of vorticity for the 2D Euler-alpha equations

David Ambrose·Milton Lopes Filho·Helena Nussenzveig Lopes

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Abstract

In this article we consider weak solutions of the Euler-$\alpha$ equations in the full plane. We take, as initial unfiltered vorticity, an arbitrary nonnegative, compactly supported, bounded Radon measure. Global well-posedness for the corresponding initial value problem is due M. Oliver and S. Shkoller. We show that, for all time, the support of the unfiltered vorticity is contained in a disk whose radius grows no faster than $\mathcal{O}((t\log t)^{1/4})$. This result is an adaptation of the corresponding result for the incompressible 2D Euler equations with initial vorticity compactly supported, nonnegative, and $p$-th power integrable, $p>2$, due to D. Iftimie, T. Sideris and P. Gamblin and, independently, to Ph. Serfati.

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David Ambrose, Milton Lopes Filho, Helena Nussenzveig Lopes. 2018-02-27. Confinement of vorticity for the 2D Euler-alpha equations. https://arxiv.org/abs/1802.10161

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