Brzezniak, Zdzislaw orcid.org/0000-0001-8731-6523, Dhariwal, Gaurav and Mariani, Mauro (2018) 2D Constrained Navier-Stokes Equations. Journal of Differential Equations. pp. 2833-2864. ISSN 0022-0396
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 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 |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 22 Jan 2018 15:50 |
Last Modified: | 02 Apr 2024 23:12 |
Published Version: | https://doi.org/10.1016/j.jde.2017.11.005 |
Status: | Published |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1016/j.jde.2017.11.005 |
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