## 2D Constrained Navier-Stokes Equations

Research output: Contribution to journalArticle

## Department/unit(s)

### Publication details

Journal Journal of Differential Equations Accepted/In press - 3 Nov 2017 E-pub ahead of print - 11 Nov 2017 Published (current) - 15 Feb 2018 4 264 32 2833-2864 11/11/17 English

### Abstract

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