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 R× 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) ⩽ Ct1 / 3log 2t when t→ ∞.