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On the existence of slow manifolds for problems with different timescales. (English) Zbl 0831.35130

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”.

MSC:

35Q30 Navier-Stokes equations
58J35 Heat and other parabolic equation methods for PDEs on manifolds
35A35 Theoretical approximation in context of PDEs
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