DETERMINATION FOR THE 2D INCOMPRESSIBLE NAVIER-STOKES EQUATIONS IN LIPSCHITZ DOMAIN

The number of determining modes is estimated for the 2D Navier-Stokes equations subject to an inhomogeneous boundary condition in Lipschitz domains by using an appropriate set of points in the configuration space to represent the flow by virtue of the Grashof number and the measure of Lipschitz boundary based on a stream function and some delicate estimates. The asymptotic determination via finite functionals for 2D autonomous Navier-Stokes equations in Lipschitz domains has been derived for the trajectories inside global attractor with finite Hausdorff dimension, which leads to this fluid flow reducing to a functional ordinary differential equation.