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 R2and 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.
2D constrained Navier–Stokes equations / Brzeźniak, Zdzisław; Dhariwal, Gaurav; Mariani, Mauro. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 264:4(2018), pp. 2833-2864. [10.1016/j.jde.2017.11.005]
2D constrained Navier–Stokes equations
Mariani, Mauro
2018
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 R2and 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.File allegati a questo prodotto
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