We study the chemotaxis–Navier–Stokes system

$ \left\{\;\; \begin{aligned} n_t + u \cdot \nabla n &\;\; = \;\; \Delta n - \nabla \cdot (nS(x,n,c) \nabla c), \\ c_t + u\cdot \nabla c &\;\; = \;\; \Delta c - n f(c), \\ u_t + (u\cdot \nabla) u &\;\; = \;\; \Delta u + \nabla P + n \nabla \phi, \;\;\;\;\;\; \nabla \cdot u = 0, \;\;\;\;\;\; \end{aligned} \right. \tag{$\star$} $

中文翻译：

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具有旋转通量分量和完整的Navier–Stokes方程的二维趋化系统的整体质量保持解

我们研究了趋化–Navier–Stokes系统

$ \ left \ {\; \; \ begin {aligned} n_t + u \ cdot \ nabla n＆\; \; = \; \; \ Delta n-\ nabla \ cdot（nS（x，n，c）\ nabla c），\\ c_t + u \ cdot \ nabla c＆\; \; = \; \; \ Delta c-nf（c），\\ u_t +（u \ cdot \ nabla）u＆\; \; = \; \; \ Delta u + \ nabla P + n \ nabla \ phi，\; \; \; \; \; \; \ nabla \ cdot u = 0，\; \; \; \; \; \; \ end {aligned} \ right。\ tag {$ \ star $} $