Multiple almost circular concentrated vortices in the 2D Euler equations remain concentrated over long time scales if they stay separated, supported by a new stability estimate for the logarithmic interaction energy.
A sharpened Riesz-Sobolev inequality
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abstract
The Riesz-Sobolev inequality provides an upper bound, in integral form, for the convolution of indicator functions of subsets of Euclidean space. We formulate and prove a sharper form of the inequality. This can be equivalently phrased as a stability result, quantifying an inverse theorem of Burchard that characterizes cases of equality.
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Long time confinement of multiple concentrated vortices
Multiple almost circular concentrated vortices in the 2D Euler equations remain concentrated over long time scales if they stay separated, supported by a new stability estimate for the logarithmic interaction energy.