On 2D Euler Equations: III. A Line Model

Abstract

The spectral theorem of the linear 2D Euler operator in Sobolev spaces is presented as a corollary of the spectral theorem in ${\ell }_2$ space in [Li,00]. Study on the (dashed) line model introduced in [Li,01] is continued. Specifically, invariant manifolds for the line model is established. The corresponding line model for 2D Navier-Stokes equation is also introduced.