2D Constrained Navier-Stokes Equations

Zdzislaw Brzezniak, Gaurav Dhariwal, Mauro Mariani

Research output: Contribution to journalArticlepeer-review


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 $\nu$
Original languageEnglish
Pages (from-to)2833-2864
Number of pages32
JournalJournal of Differential Equations
Issue number4
Early online date11 Nov 2017
Publication statusPublished - 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.


  • 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

Cite this