Global Existence of Chemotaxis-Navier–Stokes System with Logistic Source on the Whole Space R 2.

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 R 2 . [ABSTRACT FROM AUTHOR]