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

This paper is concerned with a spatially two-dimensional version of chemotaxis system logistic cell proliferation and death, for singular tactic response standard logarithmic type, interaction surrounding incompressible fluid through transport buoyancy. Systems this form are significant relevance to the understanding chemotaxis-fluid interaction, but rigorous knowledge their qualitative properties yet far from complete. In direction, using conditional energy functional method, present work provides some interesting contributions by establishing results on global boundedness, especially large time stabilization toward homogeneous equilibria, under mild assumptions initial data appropriate conditions strength damping death effects.