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In this paper, we investigate an initial-boundary value problem for achemotaxis-fluid system in a general bounded regular domain $\Omega \subset\mathbb{R}^N$ ($N\in\{2,3\}$), not necessarily being convex. Thanks to theelementary lemma given by Mizoguchi & Souplet [10], we can derive a new type ofentropy-energy estimate, which enables us to prove the following: (1) for$N=2$, there exists a unique global classical solution to the fullchemotaxis-Navier-Stokes system, which converges to a constant steady state$(n_\infty, 0,0)$ as $t\to+\infty$, and (2) for $N=3$, the existence of aglobal weak solution to the simplified chemotaxis-Stokes system. Our resultsgeneralize the recent work due to Winkler [15,16], in which the domain $\Omega$is essentially assumed to be convex.

Global Existence and Asymptotic Behavior of Solutions to a Chemotaxis-Fluid System on General Bounded Domain