On the trivial solutions for the rotating patch model

Abstract

In this paper, we study the clockwise simply connected rotating patches for Euler equations. By using the moving plane method, we prove that Rankine vortices are the only solutions to this problem in the class of slightly convex domains. We discuss in the second part of the paper the case where the angular velocity \({\varOmega=\frac{1}{2}}\), and we show without any geometric condition that the set of the V-states is trivial and reduced to the Rankine vortices.

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Correspondence to Taoufik Hmidi.

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Hmidi, T. On the trivial solutions for the rotating patch model. J. Evol. Equ. 15, 801–816 (2015). https://doi.org/10.1007/s00028-015-0281-7

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Keywords

  • Angular Velocity
  • Stream Function
  • Trivial Solution
  • Geometric Constraint
  • Convex Domain