On the De Gregorio Modification of the Constantin–Lax–Majda Model

H. Jia; S. Stewart; V. Sverak

doi:10.1007/s00205-018-1298-1

On the De Gregorio Modification of the Constantin–Lax–Majda Model

H. Jia
, S. Stewart
, V. Sverak

School of Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We study a modification due to De Gregorio of the Constantin–Lax–Majda (CLM) model ω_t = ωHω on the unit circle. The De Gregorio equation is ω_t+ uω_x- u_xω= 0 , u_x= Hω. In contrast with the CLM model, numerical simulations suggest that the solutions of the De Gregorio model with smooth initial data exist globally for all time, and generically converge to equilibria when t→ ± ∞, in a way resembling inviscid damping. We prove that such behavior takes place near a manifold of equilibria.

Original language	English (US)
Pages (from-to)	1269-1304
Number of pages	36
Journal	Archive For Rational Mechanics And Analysis
Volume	231
Issue number	2
DOIs	https://doi.org/10.1007/s00205-018-1298-1
State	Published - Feb 7 2019

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© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

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abstract = "We study a modification due to De Gregorio of the Constantin–Lax–Majda (CLM) model ωt = ωHω on the unit circle. The De Gregorio equation is ωt+ uωx- uxω= 0 , ux= Hω. In contrast with the CLM model, numerical simulations suggest that the solutions of the De Gregorio model with smooth initial data exist globally for all time, and generically converge to equilibria when t→ ± ∞, in a way resembling inviscid damping. We prove that such behavior takes place near a manifold of equilibria.",

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AU - Stewart, S.

AU - Sverak, V.

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Y1 - 2019/2/7

N2 - We study a modification due to De Gregorio of the Constantin–Lax–Majda (CLM) model ωt = ωHω on the unit circle. The De Gregorio equation is ωt+ uωx- uxω= 0 , ux= Hω. In contrast with the CLM model, numerical simulations suggest that the solutions of the De Gregorio model with smooth initial data exist globally for all time, and generically converge to equilibria when t→ ± ∞, in a way resembling inviscid damping. We prove that such behavior takes place near a manifold of equilibria.

AB - We study a modification due to De Gregorio of the Constantin–Lax–Majda (CLM) model ωt = ωHω on the unit circle. The De Gregorio equation is ωt+ uωx- uxω= 0 , ux= Hω. In contrast with the CLM model, numerical simulations suggest that the solutions of the De Gregorio model with smooth initial data exist globally for all time, and generically converge to equilibria when t→ ± ∞, in a way resembling inviscid damping. We prove that such behavior takes place near a manifold of equilibria.

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On the De Gregorio Modification of the Constantin–Lax–Majda Model

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