Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space R2

In this article, we study the Cauchy problem of the chemotaxis-Navier–Stokes system with the consumption and production of chemosignals with a logistic source. The parameters χ≠0, ξ≠0, λ>0 and μ>0. The system is a model that involves double chemosignals; one is an attractant consumed by the cells themselves, and the other is an attractant or a repellent produced by the cells themselves. We prove the global-in-time existence and uniqueness of the weak solution to the system for a large class of initial data on the whole space R2.