Convection of Microstructures by Incompressible and Slightly Compressible Flows

1986 ◽  
pp. 1-22 ◽  
Author(s):  
T. Chacon ◽  
O. Pironneau
Keyword(s):  
Compressible Flows ◽  
Slightly Compressible

On the existence of slow manifolds for problems with different timescales

1994 ◽  
Vol 346 (1679) ◽  
pp. 159-171 ◽  
Keyword(s):  
Compressible Flows ◽  
Stokes Equations ◽  
Slow Manifold ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slightly Compressible ◽  
Finite Dimensional ◽  
Uniformly Smooth ◽  
Dimensional Dynamical System

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 dynamical system will have a slow manifold.

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