Kreiss, Heinz-Otto; Lorenz, Jens On the existence of slow manifolds for problems with different timescales. (English) Zbl 0831.35130 Philos. Trans. R. Soc. Lond., Ser. A 346, No. 1679, 159-171 (1994). Authors’ summary: “We consider time dependent systems of partial differential equations (PDE) whose solutions can vary on two different timescales. An example is given by the Navier-Stokes equations for slightly compressible flows. By proper initialization, the fast timescale can be suppressed to any given order; however, this does generally not imply the existence of a slow manifold. Since the PDE solutions are uniformly smooth in space, one can approximate the PDE system by a finite dimensional Galerkin system. Under suitable assumptions, this finite dimensional system will have a slow manifold”. Reviewer: W.Velte (Würzburg) Cited in 3 Documents MSC: 35Q30 Navier-Stokes equations 58J35 Heat and other parabolic equation methods for PDEs on manifolds 35A35 Theoretical approximation in context of PDEs Keywords:Navier-Stokes equations; slow manifold; Galerkin system PDFBibTeX XMLCite \textit{H.-O. Kreiss} and \textit{J. Lorenz}, Philos. Trans. R. Soc. Lond., Ser. A 346, No. 1679, 159--171 (1994; Zbl 0831.35130) Full Text: DOI