Communications of the
Korean Mathematical Society CKMS

Considered here is the first initial boundary value problem for the two-dimensional $g$-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

Keywords: $g$-Navier-Stokes equations, global attractor, stability, stationary solution, long-time finite dimensional approximation

MSC numbers: 35B35, 35B41, 35D35, 35Q35