On the trivial solutions for the rotating patch model (Q904340)

The author studies the clockwise simply connected rotating patches for two dimensional incompressible Euler equations. By using the moving plane method, one proves that Rankine vortices are the only solutions to this problem in the class of slightly convex domains. In the second part of the paper the case where the angular velocity is 1/2 is discussed. One shows without any geometric condition that the set of the V-states is trivial and reduced to the Rankine vortices.