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Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems

V. V. ChepyzhovM. I. Vishik — 2002

ESAIM: Control, Optimisation and Calculus of Variations

We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force g ( x , t ) . We assume that g ( x , t ) is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if g ( x , t ) is a quasiperiodic function with respect to t , then the attractor is a continuous image of a torus. Moreover the...

Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems

V. V. ChepyzhovM. I. Vishik — 2010

ESAIM: Control, Optimisation and Calculus of Variations

We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force . We assume that is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if is a quasiperiodic function with respect to , then the attractor is a continuous image of a torus. Moreover ...

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