A nonlinear cross-diffusion–fluid system with chemicals terms describing the dynamics of predator–prey living in a Newtonian fluid is proposed in this paper. The existence of weak solution for the proposed macro-scale system is proved on the basis of the Schauder fixed-point theory, a priori estimates, and compactness arguments. The proposed system is derived from the underlining description delivered by a kinetic-fluid theory model by multiscale approach. Finally, we discuss the computational results for the proposed macro-scale system in two dimensional space.

中文翻译：

---

含两种化学物质的非线性捕食者-猎物交叉扩散-流体系统的数学分析和多尺度推导


本文提出了一种非线性交叉扩散流体系统，其化学术语描述了牛顿流体中捕食者-猎物的动力学。基于 Schauder 不动点理论、先验估计和紧性论证，证明了所提出的宏观尺度系统弱解的存在性。所提出的系统源自多尺度方法的运动流体理论模型所提供的强调描述。最后，我们讨论了二维空间中所提出的宏观尺度系统的计算结果。