Sergei B. Kuksin
Eulerian limit for 2D Navier-Stokes equation
and damped/driven KdV equation as its model
(264K, pdf)
ABSTRACT. We discuss the inviscid limits for the randomly forced 2D
Navier-Stokes equation and the damped/driven KdV equation. The
former describes the space-periodic 2D turbulence in terms of a
special class of solutions for the free Euler equation, and we view
the latter as its model. We review and revise recent results on the
inviscid limit for the perturbed KdV and use them to suggest a setup
which could be used to make a next step in the study of the
inviscid limit of 2D~NSE. The proposed approach is based on an
ergodic hypothesis for the flow of the 2D~Euler equation on
iso-integral surfaces. It invokes a Whitham equation for the
2D~Navier-Stokes equation, written in terms of the ergodic measures.