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
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.