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In this paper, we consider the following system $$\left\{\begin{array}{ll}n_t+u\cdot\nabla n&=\Delta n-\nabla\cdot(n\mathcal{S}(|\nabla c|^2)\nablac)-nm,\\ c_t+u\cdot\nabla c&=\Delta c-c+m,\\ m_t+u\cdot\nabla m&=\Delta m-mn,\\u_t&=\Delta u+\nabla P+(n+m)\nabla\Phi,\qquad \nabla\cdot u=0\end{array}\right.$$ which models the process of coral fertilization, in asmoothly three-dimensional bounded domain, where $\mathcal{S}$ is a givenfunction fulfilling $$|\mathcal{S}(\sigma)|\leqK_{\mathcal{S}}(1+\sigma)^{-\frac{\theta}{2}},\qquad \sigma\geq 0$$ with some$K_{\mathcal{S}}>0.$ Based on conditional estimates of the quantity $c$ and thegradients thereof, a relatively compressed argument as compared to thatproceeding in related precedents shows that if $$\theta>0,$$ then for anyinitial data with proper regularity an associated initial-boundary problemunder no-flux/no-flux/no-flux/Dirichlet boundary conditions admits a uniqueclassical solution which is globally bounded, and which also enjoys thestabilization features in the sense that$$\|n(\cdot,t)-n_{\infty}\|_{L^{\infty}(\Omega)}+\|c(\cdot,t)-m_{\infty}\|_{W^{1,\infty}(\Omega)}+\|m(\cdot,t)-m_{\infty}\|_{W^{1,\infty}(\Omega)}+\|u(\cdot,t)\|_{L^{\infty}(\Omega)}\rightarrow0\quad\textrm{as}~t\rightarrow \infty$$ with$n_{\infty}:=\frac{1}{|\Omega|}\left\{\int_{\Omega}n_0-\int_{\Omega}m_0\right\}_{+}$and$m_{\infty}:=\frac{1}{|\Omega|}\left\{\int_{\Omega}m_0-\int_{\Omega}n_0\right\}_{+}.$

Influence of flux limitation on large time behavior in a three-dimensional chemotaxis-Stokes system modeling coral fertilization