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On the existence of pullback attractor for a two-dimensional shear flow with Tresca's boundary condition

100%

Boukrouche M., Łukaszewicz G.

Banach Center Publications

2008

tom 81

nr 1

81-93

We consider a two-dimensional Navier-Stokes shear flow with time dependent boundary driving and subject to Tresca law. We establish the existence of a unique global in time solution and then, using a recent method based on the concept of the Kuratowski measure of noncompactness of a bounded set, we prove the existence of the pullback attractor for the associated cocycle. This research is motivated by a problem from lubrication theory.

An upper bound on the attractor dimension of a 2D turbulent shear flow with a free boundary condition

100%

Boukrouche M., Łukaszewicz G.

Banach Center Publications

2005

tom 70

nr 1

61-72

We consider a free boundary problem of a two-dimensional Navier-Stokes shear flow. There exist a unique global in time solution of the considered problem as well as the global attractor for the associated semigroup. As in [1] and [2], we estimate from above the dimension of the attractor in terms of given data and the geometry of the domain of the flow. This research is motivated by a free boundary problem from lubrication theory where the domain of the flow is usually very thin and the roughness of the boundary strongly affects the flow. We show how it can enlarge the dimension of the attractor. To this end we establish a new version of the Lieb-Thirring inequality with constants depending on the geometry of the domain.

Ograniczanie wyników

2 Banach Center Publications

2 Boukrouche M.

2 Łukaszewicz G.

1 2008

1 2005

Wyniki wyszukiwania

On the existence of pullback attractor for a two-dimensional shear flow with Tresca's boundary condition

An upper bound on the attractor dimension of a 2D turbulent shear flow with a free boundary condition