On the dimension of the attractor for the non-homogeneous Navier-Stokes equations in non-smooth domains

Authors
Brown, RM Perry, PA Shen, ZW
Citation
Rm. Brown et al., On the dimension of the attractor for the non-homogeneous Navier-Stokes equations in non-smooth domains, INDI MATH J, 49(1), 2000, pp. 81-112
Citations number
16
Categorie Soggetti
Mathematics
Journal title
INDIANA UNIVERSITY MATHEMATICS JOURNAL
ISSN journal
00222518 → ACNP
Volume
49
Issue
1
Year of publication
2000
Pages
81 - 112
Database
ISI
SICI code
0022-2518(200021)49:1<81:OTDOTA>2.0.ZU;2-J
Abstract
This paper concerns the two-dimensional Navier-Stokes equations in a Lipsch itz domain Omega with nonhomogeneous boundary condition u = phi on partial derivative Omega. Assuming phi is an element of L-infinity(partial derivati ve Omega), we establish the existence of the universal attractor, and show that its dimension is bounded by c(1)G + c(2)Re(3/2), where G is the Grasho f number and Re the Reynolds number.