Vorticity near point vortices on the rotating sphere shows logarithmic confinement in time, improbability of collisions, and power-law confinement in some cases.
Desingularization of time-periodic vortex motion in bounded domains via KAM tools
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Computer-assisted proof shows that the linearized operator around threefold symmetric traveling waves in the Burgers-Hilbert equation has an eigenvalue with negative real part for ω=3 and c≈1.1.
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.
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Confinement results near point vortices on the rotating sphere
Vorticity near point vortices on the rotating sphere shows logarithmic confinement in time, improbability of collisions, and power-law confinement in some cases.
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Linear instability of a Burgers--Hilbert traveling wave
Computer-assisted proof shows that the linearized operator around threefold symmetric traveling waves in the Burgers-Hilbert equation has an eigenvalue with negative real part for ω=3 and c≈1.1.