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

Wenlong Sun, Yeping Li

DOI: http://dx.doi.org/10.12775/TMNA.2017.024

Abstract


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.

Keywords


Keller-Segel-Stokes model; trajectory attractor; global attractor; translation semigroup

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