Global-attractor conjecture for anisotropic micropolar fluids

Let $\lambda$ and $\nu$ be the two eigenvalues of the planar microinertia block, with the microstructure called inertially oblong when $\lambda>\nu$ and inertially oblate when $\lambda<\nu$. Consider the anisotropic micropolar-fluid evolution system

$$--.$$

The energetic equilibria and their orbit are those identified in Proposition $\mathrm{}$. Global-attractor conjecture. If the microstructure is inertially oblong, $\lambda>\nu$, then the orbit of energetic equilibria is the global attractor of the system. If the microstructure is inertially oblate, $\lambda<\nu$, then the equilibrium identified in Proposition $\mathrm{}$ is the global attractor of the system. The conjecture proposes a characterization of the global attractor in terms of the equilibrium and the orbit of energetic equilibria; the source provides no resolution, so the claim remains open.