## 2D Constrained Navier-Stokes Equations

Research output: Contribution to journalArticle

### Standard

2D Constrained Navier-Stokes Equations. / Brzezniak, Zdzislaw; Dhariwal, Gaurav; Mariani, Mauro.

In: Journal of Differential Equations, Vol. 264, No. 4, 15.02.2018, p. 2833-2864.

Research output: Contribution to journalArticle

### Harvard

Brzezniak, Z, Dhariwal, G & Mariani, M 2018, '2D Constrained Navier-Stokes Equations', Journal of Differential Equations, vol. 264, no. 4, pp. 2833-2864.

### APA

Brzezniak, Z., Dhariwal, G., & Mariani, M. (2018). 2D Constrained Navier-Stokes Equations. Journal of Differential Equations, 264(4), 2833-2864.

### Vancouver

Brzezniak Z, Dhariwal G, Mariani M. 2D Constrained Navier-Stokes Equations. Journal of Differential Equations. 2018 Feb 15;264(4):2833-2864.

### Author

Brzezniak, Zdzislaw ; Dhariwal, Gaurav ; Mariani, Mauro. / 2D Constrained Navier-Stokes Equations. In: Journal of Differential Equations. 2018 ; Vol. 264, No. 4. pp. 2833-2864.

@article{469ec257003a4cecbe12cddf79897172,
title = "2D Constrained Navier-Stokes Equations",
abstract = "We study 2D Navier-Stokes equations with a constraint forcing theconservation of the energy of the solution. We prove the existence anduniqueness of a global solution for the constrained Navier-Stokesequation on $\mathbb{R}^2$ and $\mathbb{T}^2$, by a fixed pointargument. We also show that the solution of the constrained equationconverges to the solution of the Euler equation as the viscosity $\nu$vanishes.",
keywords = "Navier-Stokes Equations, constrained energy, periodic boundary conditions, gradient flow , global solution , convergence, Euler Equations",
author = "Zdzislaw Brzezniak and Gaurav Dhariwal and Mauro Mariani",
note = "{\circledC} 2017 Elsevier Inc. All rights reserved. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.",
year = "2018",
month = "2",
day = "15",
language = "English",
volume = "264",
pages = "2833--2864",
journal = "Journal of Differential Equations",
issn = "0022-0396",
number = "4",

}

TY - JOUR

T1 - 2D Constrained Navier-Stokes Equations

AU - Brzezniak, Zdzislaw

AU - Dhariwal, Gaurav

AU - Mariani, Mauro

PY - 2018/2/15

Y1 - 2018/2/15

N2 - We study 2D Navier-Stokes equations with a constraint forcing theconservation of the energy of the solution. We prove the existence anduniqueness of a global solution for the constrained Navier-Stokesequation on $\mathbb{R}^2$ and $\mathbb{T}^2$, by a fixed pointargument. We also show that the solution of the constrained equationconverges to the solution of the Euler equation as the viscosity $\nu$vanishes.

AB - We study 2D Navier-Stokes equations with a constraint forcing theconservation of the energy of the solution. We prove the existence anduniqueness of a global solution for the constrained Navier-Stokesequation on $\mathbb{R}^2$ and $\mathbb{T}^2$, by a fixed pointargument. We also show that the solution of the constrained equationconverges to the solution of the Euler equation as the viscosity $\nu$vanishes.

KW - Navier-Stokes Equations

KW - constrained energy

KW - periodic boundary conditions

KW - global solution

KW - convergence

KW - Euler Equations

M3 - Article

VL - 264

SP - 2833

EP - 2864

JO - Journal of Differential Equations

T2 - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 4

ER -