### 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 L^{2} 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 language | English (US) |
---|---|

Article number | abt009 |

Pages (from-to) | 157-175 |

Number of pages | 19 |

Journal | Applied Mathematics Research eXpress |

Volume | 2014 |

Issue number | 1 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Computational Mathematics

### Cite this

*Applied Mathematics Research eXpress*,

*2014*(1), 157-175. [abt009]. https://doi.org/10.1093/amrx/abt009

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

Research output: Contribution to journal › Article

*Applied Mathematics Research eXpress*, vol. 2014, no. 1, abt009, pp. 157-175. https://doi.org/10.1093/amrx/abt009

}

TY - JOUR

T1 - Asymptotic stability for the couette flow in the 2d euler equations

AU - Bedrossian, Jacob

AU - Masmoudi, Nader

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84896355087&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84896355087&partnerID=8YFLogxK

U2 - 10.1093/amrx/abt009

DO - 10.1093/amrx/abt009

M3 - Article

VL - 2014

SP - 157

EP - 175

JO - Applied Mathematics Research eXpress

JF - Applied Mathematics Research eXpress

SN - 1687-1200

IS - 1

M1 - abt009

ER -