  In this paper, we consider the following system $$\left\{\begin{array}{ll}
n_t+u\cdot\nabla n&=\Delta n-\nabla\cdot(n\mathcal{S}(|\nabla c|^2)\nabla
c)-nm,\\ c_t+u\cdot\nabla c&=\Delta c-c+m,\\ m_t+u\cdot\nabla m&=\Delta m-mn,\\
u_t&=\Delta u+\nabla P+(n+m)\nabla\Phi,\qquad \nabla\cdot u=0
\end{array}\right.$$ which models the process of coral fertilization, in a
smoothly three-dimensional bounded domain, where $\mathcal{S}$ is a given
function fulfilling $$|\mathcal{S}(\sigma)|\leq
K_{\mathcal{S}}(1+\sigma)^{-\frac{\theta}{2}},\qquad \sigma\geq 0$$ with some
$K_{\mathcal{S}}>0.$ Based on conditional estimates of the quantity $c$ and the
gradients thereof, a relatively compressed argument as compared to that
proceeding in related precedents shows that if $$\theta>0,$$ then for any
initial data with proper regularity an associated initial-boundary problem
under no-flux/no-flux/no-flux/Dirichlet boundary conditions admits a unique
classical solution which is globally bounded, and which also enjoys the
stabilization 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
$m_{\infty}:=\frac{1}{|\Omega|}\left\{\int_{\Omega}m_0-\int_{\Omega}n_0\right\}_{+}.$
