May 8, 2009: Hantaek Bae, CIMS
Inviscid limit for damped and driven incompressible NavierStokes equations in $R^{2}$
Recently, ConstantinRamos consider the zero viscosity limit of long time averages of solutions of damped and driven NavierStokes equations in $R^{2}$ in the vorticity equation. They proved that the rate of dissipation of enstrophy vanishes. Statistical stationary solutions of the damped and driven NavierStokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstrophy balance. As an application, Constantin suggested the same question of absence of anomalous dissipation of the kinetic energy to the quasigeostrophic equations. I will explain why this question is much harder for the quasigeostrophic equations.
Reference: P. Constantin, F. Ramos : Inviscid limit for damped and driven incompressible NavierStokes equations in $R^{2}$, Commun. Math. Phys, 275(2007), pp.529551
