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

Mahdi 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 -