We consider an attraction-repulsion chemotaxis model in the whole space \({\mathbb {R}}^3\) with logistic source coupled with the incompressible Navier–Stokes equations. By means of a contraction argument, we obtain the existence and uniqueness of global mild solutions in a framework of Besov type, namely Besov spaces based on Morrey spaces. In comparison with previous results for the system dealt with, that framework provides new solutions and allows us to consider larger initial data and force classes for global existence and uniqueness. To carry out our results, we prove some essential lemmas and estimates related to the heat semigroup and continuity properties for the Bony decomposition in our setting.

我们考虑在全空间\（{{\ mathbb {R}} ^ 3 \）中的吸引排斥趋化模型，其中逻辑源与不可压缩的Navier–Stokes方程相结合。通过收缩论证，我们获得了Besov类型框架（即基于Morrey空间的Besov空间）中全局温和解的存在性和唯一性。与处理该系统的先前结果相比，该框架提供了新的解决方案，使我们可以考虑使用更大的初始数据并为全球存在和唯一性强制使用类别。为了执行我们的结果，我们证明了一些与我们的环境中Bony分解的热半群和连续性有关的引理和估计。