In this paper, we study a two-species chemotaxis–fluid system with Lotka–Volterra type competitive kinetics in a bounded and smooth domain $\mathrm{\Omega }\subset {ℝ}^3$ with no-flux/Dirichlet boundary conditions. We present the global existence of weak energy solution to a two-species chemotaxis Navier–Stokes system, and then the global weak energy solution which coincides with a smooth function throughout $\overline{\mathrm{\Omega }}\times \mathrm{\Pi }$, where $\mathrm{\Pi }$ represents a countable union of open intervals which is such that $|(0,\infty )\setminus \mathrm{\Pi }|=0$. In such two-species chemotaxis–fluid setting, our existence improves known blow-up prevention by logistic source to blow-up prevention by sub-logistic source, indicating standard logistic source is not the weakest damping source to prevent blow-up. This finding significantly extends previously known ones.

在本文中，我们研究了在有界且光滑的域中具有 Lotka-Volterra 型竞争动力学的两种物种趋化性流体系统$\mathrm{\Omega }\subset {ℝ}^3$具有无通量/狄利克雷边界条件。我们提出了两种物种趋化性纳维-斯托克斯系统的弱能解的全局存在性，然后提出了与整个平滑函数一致的全局弱能解$\stackrel{￣}{\mathrm{\Omega }}\times \mathrm{\Pi }$， 在哪里$\mathrm{\Pi }$表示开区间的可数并集，使得$|（0,\mathrm{无穷大}）\setminus \mathrm{\Pi }|=0$。在这种两种趋化性流体环境中，我们的存在将已知的逻辑源的爆炸预防改进为子逻辑源的爆炸预防，这表明标准逻辑源并不是防止爆炸的最弱阻尼源。这一发现显着扩展了之前已知的发现。