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

Mahdi Boukrouche; Grzegorz Łukaszewicz

Banach Center Publications (2005)

- Volume: 70, Issue: 1, page 61-72
- ISSN: 0137-6934

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topMahdi Boukrouche, and Grzegorz Łukaszewicz. "An upper bound on the attractor dimension of a 2D turbulent shear flow with a free boundary condition." Banach Center Publications 70.1 (2005): 61-72. <http://eudml.org/doc/282579>.

@article{MahdiBoukrouche2005,

abstract = {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.},

author = {Mahdi Boukrouche, Grzegorz Łukaszewicz},

journal = {Banach Center Publications},

keywords = {Navier-Stokes equations; lubrication theory; global solution; energy dissipation rate; global attractor; Lieb-Thirring inequality},

language = {eng},

number = {1},

pages = {61-72},

title = {An upper bound on the attractor dimension of a 2D turbulent shear flow with a free boundary condition},

url = {http://eudml.org/doc/282579},

volume = {70},

year = {2005},

}

TY - JOUR

AU - Mahdi Boukrouche

AU - Grzegorz Łukaszewicz

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

JO - Banach Center Publications

PY - 2005

VL - 70

IS - 1

SP - 61

EP - 72

AB - 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.

LA - eng

KW - Navier-Stokes equations; lubrication theory; global solution; energy dissipation rate; global attractor; Lieb-Thirring inequality

UR - http://eudml.org/doc/282579

ER -

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