Asymptotic profile of a two-dimensional Chemotaxis–Navier–Stokes system with singular sensitivity and logistic source

Abstract

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.