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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For frequency ω=3 and wave speed c≈1.1, the linearized operator around Burgers-Hilbert traveling waves has an eigenvalue with negative real part, shown via computer-assisted interval arithmetic.
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.
citing papers explorer
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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
For frequency ω=3 and wave speed c≈1.1, the linearized operator around Burgers-Hilbert traveling waves has an eigenvalue with negative real part, shown via computer-assisted interval arithmetic.
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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.