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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 2833-2864 |
| Number of pages | 32 |
| Journal | Journal of Differential Equations |
| Volume | 264 |
| Issue number | 4 |
| Early online date | 11 Nov 2017 |
| DOIs | |
| Publication status | Published - 15 Feb 2018 |
Bibliographical note
© 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.Keywords
- Navier-Stokes Equations
- constrained energy
- periodic boundary conditions
- gradient flow
- global solution
- convergence
- Euler Equations
- Navier–Stokes equations
- Constrained energy
- Periodic boundary conditions
- Euler equations
- Gradient flow