Grad Student/Postdoc Seminar

May 8, 2009:  Hantaek Bae, CIMS

Inviscid limit for damped and driven incompressible Navier-Stokes equations in $R^{2}$
  

  Recently, Constantin-Ramos consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes 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 Navier-Stokes 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 quasi-geostrophic equations. I will explain why this question is much harder for the quasi-geostrophic equations.

Reference: P. Constantin, F. Ramos : Inviscid limit for damped and driven incompressible Navier-Stokes equations in $R^{2}$, Commun. Math. Phys, 275(2007), pp.529-551
 


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