2D Constrained Navier-Stokes Equations

Abstract

We study 2D Navier-Stokes equations with a constraint on $L^2$ 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 $\T$, by a fixed point argument. We also show that the solution of constrained Navier-Stokes converges to the solution of Euler equation as viscosity $\nu$ vanishes.

Cited by in corpus (4)

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• Stochastic Navier-Stokes equations on a thin spherical domain
• Existence and asymptotic behavior for $L^2$-norm preserving nonlinear heat equations
• Stochastic Constrained Navier-Stokes Equations on ${\mathbb{T}}^2$