Global existence and stabilization in a two-dimensional chemotaxis-Navier-Stokes system with consumption and production of chemosignals

Abstract

We are concerned with the initial boundary value problems of chemotaxis-Navier-Stokes systems involving 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. This work reveals that for any properly regular initial data, if the initial total cells mass is less than some threshold, then the corresponding attraction-atraction Navier-Stokes system admits a unique global classical solution, which, under extra two smallness assumptions on the initial data, is globally bounded and converges at exponential rate to the spatial equilibrium in the large time limit. As byproducts, the global classical solvability and stabilization of the Keller-Segel Navier-Stokes system and the uniform boundedness and large time behavior of the global classical solution of the associated attraction-repulsion Navier-Stokes system are simultaneously achieved.