The unstable spectrum of the Navier–Stokes operator in the limit of vanishing viscosity

The Navier–Stokes equations for the motion of an incompressible fluid in three dimensions are considered. A partition of the evolution operator into high frequency and low frequency parts is derived. This decomposition is used to prove that the eigenvalues of the Navier–Stokes operator in the inviscid limit converge precisely to the eigenvalues of the Euler operator beyond the essential spectrum.