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

This paper concerns the two-dimensional Navier-Stokes equations in a Lipschitz domain Ω with nonhomogeneous boundary condition u = φ on ∂Ω. Assuming φ ∈ L∞ (∂Ω), we establish the existence of the universal attractor, and show that its dimension is bounded by c₁G + c₂Re^3/2, where G is the Grashof number and Re the Reynolds number.