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

• Autorzy: Mahdi Boukrouche , Grzegorz Łukaszewicz
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35R35: Free boundary problems
• 76F10: Shear flows

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2005
• Tom: 70
• Numer: 1
• Strony: 61-72

Daty

wydano

2005

Twórcy

autor

Mahdi Boukrouche

• Laboratory of Mathematics, University of Saint-Étienne, EA-3989, 23 rue du Dr Paul Michelon, 42023 Saint-Étienne, France

autor

Grzegorz Łukaszewicz

• Mathematics Department, University of Warsaw, Banacha 2, 02-957 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc70-0-4