Plot for b(x) = (2 + cos(8πx))e i2πx (left), and b(x) = exp 2iπ(x + 1 8 cos(6πx) 3 2 + 1 4 cos(6πx)

Plot for b(x) = (2 + cos(8πx))e i2πx (left), and b(x) = exp 2iπ(x + 1 8 cos(6πx) 3 2 + 1 4 cos(6πx)

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In this paper we consider the incompressible Euler equation in a simply-connected bounded planar domain. We study the confinement of the vorticity around a stationary point vortex. We show that the power law confinement around the center of the unit disk obtained in [2] remains true in the case of a stationary point vortex in a simply-connected bou...

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... that these domains don't necessarily have symmetry properties. Finally, by using the rotational invariance property, we can plot more complicated boundaries without knowing the biholomorphic map, like in figure 5. We plotted images of the interval [0,1] by maps of the form b(x) = r(x)e i2π(x+θ(x)) , with r(x) > 0. We choose θ and r to be 1/p-periodic functions with p > 2 an integer. ...