On the growth of the support of positive vorticity for 2D Euler equation in an infinite cylinder

Abstract

We consider the incompressible 2D Euler equation in an infinite cylinder $\mathbb{R}\times \mathbb{T}$ in the case when the initial vorticity is non-negative, bounded, and compactly supported. We study $d(t)$, the diameter of the support of vorticity, and prove that it allows the following bound: $d(t)\le C{t}^{1/3}{\log }^{2}t$ when $t\to \infty$.

14 pages

Cited by in corpus (2)

• Stability of monotone, non-negative, and compactly supported vorticities in the half cylinder and infinite perimeter growth for patches
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