This paper deals with a two-chemical reaction type Keller-Segel system coupled with incompressible viscous fluid equations which models the dynamics of cells in fluid in a two dimensional bounded domain \(\varOmega \)$$ \left\{ \textstyle\begin{array}{l} \partial _{t}n+\mathbf {u}\cdot \nabla n = \Delta n - \nabla \cdot \bigl(n\chi(n,v,w,x)\nabla v\bigr), \\ \partial _{t}v+\mathbf {u}\cdot \nabla v= \Delta v -v + w, \\ \partial _{t}w+\mathbf {u}\cdot \nabla w = \Delta w -w + n, \\ \partial _{t}\mathbf {u}+ \nabla P = \Delta \mathbf {u}+ n\nabla \psi, \quad \nabla \cdot \mathbf {u}= 0. \end{array}\displaystyle \right. $$Here, \(\chi(n,v,w,x)\) represents the saturated sensitivity. Our result suggests that suitable saturation can prevent the blow-up arising from the classical Keller-Segel type signal production mechanism without any smallness condition on initial mass.

中文翻译：

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在二维Keller-Segel-Stokes系统中通过饱和趋化敏感性防止爆炸

本文研究的是两化学反应类型的Keller-Segel系统，结合不可压缩的粘性流体方程，该方程在二维有界域中模拟流体中细胞的动力学\（\ varOmega \）$$ \ left \ {\ textstyle \ begin {array} {l} \ partial _ {t} n + \ mathbf {u} \ cdot \ nabla n = \ Delta n-\ nabla \ cdot \ bigl（n \ chi（n，v，w，x）\ nabla v \ bigr），\\ \ partial _ {t} v + \ mathbf {u} \ cdot \ nabla v = \ Delta v -v + w，\\ \ partial _ {t} w + \ mathbf {u} \ cdot \ nabla w = \ Delta w -w + n，\\ \ partial _ {t} \ mathbf {u} + \ nabla P = \ Delta \ mathbf {u} + n \ nabla \ psi，\ quad \ nabla \ cdot \ mathbf {u} =0。\ end {array} \ displaystyle \ right。$$在这里\（\ chi（n，v，w，x）\）代表饱和灵敏度。我们的结果表明，适当的饱和度可以防止经典的Keller-Segel型信号产生机制引起的爆炸，而对初始质量没有任何小限制。