This paper is concerned with a chemotaxis-Stokes system modeling coral fertilization in a spatially 3D bounded domain with smooth boundary, where \(m>0\) , \(S\in C^2(\bar{\Omega }\times [0,\infty )^2; \mathbb {R}^{3\times 3})\) is a rotation satisfying \(|S(x,n,v)|\le S_0(v)(1+n)^{-\alpha }\) with some nondecreasing and nonnegative function \(S_0\) and \(\alpha \in \mathbb {R}\) , \(\phi \in W^{2,\infty }(\Omega )\) is the gravitational potential. Given some sufficiently smooth initial data and no-flux/no-flux/no-flux/Dirichlet boundary conditions, it is proved that the mild requirement \(m+\alpha >1\) with \(m>0\) and \(\alpha \in \mathbb {R}\) is sufficient to ensure the global boundedness of the corresponding initial-boundary value problem to system ( \(*\) ), which improved many known results. To our knowledge, this is the mildest condition on parameters m and \(\alpha \) so far warranting the boundedness to the 3D version of system ( \(*\) ) without any smallness assumption on the initial data.
