Trajectory attractor and global attractor for Keller-Segel-Stokes model with arbitrary porous medium diffusion

We investigate long-time behavior of weak solutions for the Keller-Segel-Stokes model with arbitrary porous medium diffusion in 2D bounded domains. We first prove the existence of the trajectory attractor $\mathcal{A}^{\text{\rm tr}}$ for the translation semigroup in the trajectory space. Further, we construct the global attractor $\mathcal{A}$ in a generalized sense. The results are shown by the definition of trajectory attractor and global attractor, and energy estimates.