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

H. Jia, S. Stewart, V. Sverak

Research output: Contribution to journalArticle

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1269-1304
Number of pages36
JournalArchive For Rational Mechanics And Analysis
Volume231
Issue number2
DOIs
StatePublished - Feb 7 2019

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