We consider an initial-boundary value problem for the incompressible four-component Keller-Segel-Navier-Stokes system with rotational flux

$ \begin{align} \left\{ \begin{array}{l} n_t+u\cdot\nabla n = \Delta n-\nabla\cdot(nS(x,n,c)\nabla c)-nm,\quad x\in \Omega, t>0,\\ c_t+u\cdot\nabla c = \Delta c-c+m,\quad x\in \Omega, t>0,\\ m_t+u\cdot\nabla m = \Delta m-nm,\quad x\in \Omega, t>0, \qquad \qquad \qquad \qquad \qquad \qquad (*)\\ u_t+\kappa(u \cdot \nabla)u+\nabla P = \Delta u+(n+m)\nabla \phi,\quad x\in \Omega, t>0,\\ \nabla\cdot u = 0,\quad x\in \Omega, t>0\\ \end{array}\right. \end{align} $

中文翻译：

---

三维Keller-Segel-Navier-Stokes系统模拟珊瑚施肥的整体弱解

我们考虑具有旋转通量的不可压缩四分量Keller-Segel-Navier-Stokes系统的初边值问题

$ \ begin {align} \ left \ {\ begin {array} {l} n_t + u \ cdot \ nabla n = \ Delta n- \ nabla \ cdot（nS（x，n，c）\ nabla c）-nm ，\ quad x \ in \ Omega，t> 0，\\ c_t + u \ cdot \ nabla c = \ Delta c-c + m，\ quad x \ in \ Omega，t> 0，\\ m_t + u \ cdot \ nabla m = \ Delta m-nm，\ quad x \ in \ Omega，t> 0，\ qquad \ qquad \ qquad \ qquad \ qquad \ qquad（*）\\ u_t + \ kappa（u \ cdot \ nabla） u + \ nabla P = \ Delta u +（n + m）\ nabla \ phi，\ quad x \ in \ Omega，t> 0，\\ \ nabla \ cdot u = 0，\ quad x \ in \ Omega，t> 0 \\ \ end {array} \ right。\ end {align} $