This paper is concerned with a spatially two-dimensional version of a chemotaxis system with logistic cell proliferation and death, for a singular tactic response of standard logarithmic type, and with interaction with a surrounding incompressible fluid through transport and buoyancy. Systems of this form are of significant relevance to the understanding of chemotaxis-fluid interaction, but the rigorous knowledge of their qualitative properties is yet far from complete. In this direction, using the conditional energy functional method, the present work provides some interesting contributions by establishing results on global boundedness, and especially on large time stabilization toward homogeneous equilibria, under mild assumptions on the initial data and appropriate conditions on the strength of the damping death effects.

中文翻译：

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具有奇异灵敏度和逻辑源的二维趋化性-Navier-Stokes 系统的渐近分布

本文关注具有逻辑细胞增殖和死亡的空间二维版本的趋化系统，用于标准对数类型的奇异策略响应，以及通过运输和浮力与周围不可压缩流体的相互作用。这种形式的系统与对趋化性-流体相互作用的理解具有重要意义，但对其定性特性的严格了解还远未完成。在这个方向上，使用条件能量泛函方法，目前的工作通过建立关于全局有界性的结果，特别是关于均匀均衡的大时间稳定性，在对初始数据和适当条件的温和假设下，提供了一些有趣的贡献。抑制死亡效应。