2D Constrained Navier-Stokes Equations
  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 $\R^2$ 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. 
Zdzis{\l}aw Brze\'zniak, Gaurav Dhariwal, Mauro Mariani
math.AP