We consider a 2D vorticity configuration where vorticity is highly concentrated around a curve and exponentially decaying away from it: the intensity of the vorticity is $O(1/epsilon)$ on the curve while it decays on an $O(epsilon)$ distance from the curve itself. We prove that, if the initial datum is of vortex-layer type, Euler solutions preserve this structure for a time which does not depend on $epsilon$. Moreover the motion of the center of the layer is well approximated by the Birkhoff-Rott equation.

R.E. Caflisch, M.C. Lombardo, M. Sammartino (2020). Vortex layers of small thickness. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS(10), 2104-2179 [10.1002/cpa.21897].

Vortex layers of small thickness

M. C. Lombardo;M. Sammartino
2020-01-01

Abstract

We consider a 2D vorticity configuration where vorticity is highly concentrated around a curve and exponentially decaying away from it: the intensity of the vorticity is $O(1/epsilon)$ on the curve while it decays on an $O(epsilon)$ distance from the curve itself. We prove that, if the initial datum is of vortex-layer type, Euler solutions preserve this structure for a time which does not depend on $epsilon$. Moreover the motion of the center of the layer is well approximated by the Birkhoff-Rott equation.
Settore MAT/07 - Fisica Matematica
R.E. Caflisch, M.C. Lombardo, M. Sammartino (2020). Vortex layers of small thickness. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS(10), 2104-2179 [10.1002/cpa.21897].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/386700
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