  The paper gives sharp spectral gap conditions for existence of inertial
manifolds for abstract semilinear parabolic equations with non-self-adjoint
leading part. Main attention is paid to the case where this leading part have
Jordan cells which appear after applying the so-called Kwak transform to
various important equations such as 2D Navier-Stokes equations,
reaction-diffusion-advection systems, etc. The different forms of Kwak
transforms and relations between them are also discussed.
