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2D Constrained Navier-Stokes Equations

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JournalJournal of Differential Equations
DateAccepted/In press - 3 Nov 2017
DateE-pub ahead of print - 11 Nov 2017
DatePublished (current) - 15 Feb 2018
Issue number4
Volume264
Number of pages32
Pages (from-to)2833-2864
Early online date11/11/17
Original languageEnglish

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.

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© 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.

    Research areas

  • Navier-Stokes Equations, constrained energy, periodic boundary conditions, gradient flow , global solution , convergence, Euler Equations

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