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On the Growth of the Support of Positive Vorticity for 2D Euler Equation in an Infinite Cylinder

  • Kyudong ChoiEmail author
  • Sergey Denisov
Article
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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: \({d(t) \leqslant Ct^{1/3}{\rm log}^{2}t}\) when \({t \to \infty}\).

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Notes

Acknowledgements

The work of KC was supported by NRF-2015R1D1A1A01058614, by the POSCO Science Fellowship of POSCO TJ Park Foundation, and by the Research Fund (1.170045.01) of UNIST (Ulsan National Institute of Science and Technology). The work of SD on the first three sections was supported by RSF-14-21-00025 and his research on the rest of the paper was supported by NSF Grant DMS-1464479.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUlsan National Institute of Science and TechnologyUlsanRepublic of Korea
  2. 2.Mathematics DepartmentUniversity of Wisconsin–MadisonMadisonUSA
  3. 3.Keldysh Institute for Applied MathematicsRussian Academy of SciencesMoscowRussia

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