We study slow flocking phenomenon arising from the dynamics of Cucker-Smale (CS) ensemble with chemotactic movements in a self-consistent temperature field. For constant temperature field, our situation reduces to the previous CS model with chemotactic movements. When a large CS ensemble with chemotactic movements is placed in a self-consistent temperature field, the dynamics of the CS ensemble can be effectively described by the kinetic thermodynamic CS (TCS) equation with chemotactic movements, which corresponds to the coupled collisional transport-reaction diffusion system. For the proposed coupled model, we provide a global solvability of strong solutions and their asymptotic flocking estimates which exhibit slow algebraic relaxation toward the flocking state. Our analytical results show that asymptotic flocking is robust with respect to a small perturbation of a constant temperature.

中文翻译：

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在温度场中具有趋化运动的Cucker-Smale合奏的植绒动力学缓慢

我们研究了在自洽温度场中由趋化运动导致的Cucker-Smale（CS）合奏动力学引起的缓慢植绒现象。对于恒定温度场，我们的情况可以简化为先前具有趋化运动的CS模型。当将具有趋化运动的大型CS集成体放置在自洽温度场中时，可以通过具有趋化运动的动力学热力学CS（TCS）方程有效地描述CS集成体的动力学，该方程对应于耦合的碰撞迁移反应扩散系统。对于提出的耦合模型，我们提供了强解的整体可解性及其渐近的植绒估计，这些估计对植绒状态表现出缓慢的代数松弛。