Asymptotic stability for the couette flow in the 2d euler equations

Jacob Bedrossian, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

In this expository note, we discuss our recent work [7] on the nonlinear asymptotic stability of shear flows in the 2D Euler equations of ideal, incompressible flow. In that work, it is proved that perturbations to the Couette flow which are small in a suitable regularity class converge strongly in L2 to a shear flow which is close to the Couette flow. Enstrophy is mixed to small scales by an almost linear evolution and is generally lost in the weak limit as. In this note, we discuss the most important physical and mathematical aspects of the result and the key ideas of the proof.

Original languageEnglish (US)
Article numberabt009
Pages (from-to)157-175
Number of pages19
JournalApplied Mathematics Research eXpress
Volume2014
Issue number1
DOIs
StatePublished - 2014

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Couette Flow
Euler equations
Shear flow
Shear Flow
Asymptotic stability
Euler Equations
Asymptotic Stability
Weak Limit
Incompressible flow
Nonlinear Stability
Incompressible Flow
Regularity
Perturbation
Converge
Class

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

Asymptotic stability for the couette flow in the 2d euler equations. / Bedrossian, Jacob; Masmoudi, Nader.

In: Applied Mathematics Research eXpress, Vol. 2014, No. 1, abt009, 2014, p. 157-175.

Research output: Contribution to journalArticle

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