2D constrained Navier–Stokes equations

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 R2 and T2, by a fixed point argument. We also show that the solution of the constrain...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 264; no. 4; pp. 2833 - 2864
Main Authors Brzeźniak, Zdzisław, Dhariwal, Gaurav, Mariani, Mauro
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.02.2018
Subjects
Constrained energy
Euler equations
Gradient flow
Navier–Stokes equations
Periodic boundary conditions
secondary
Navier–Stokes equations
Constrained energy
Periodic boundary conditions
Gradient flow
Euler equations
primary
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Summary: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 R2 and T2, 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 ν vanishes.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2017.11.005