Boundedness of solutions to a 2D chemotaxis-Navier–Stokes system with general sensitivity and nonlinear diffusion

Abstract

This paper deals with the chemotaxis-Navier–Stokes system with the density equation nt+u⋅∇n=Δnm−∇⋅(nS(x,n,c)∇c)in a bounded domain Ω⊂R2. This paper gives results for global existence, boundedness and stabilization of solutions to the system provided that m>1+4α3,|S(x,n,c)|≤S0nα,S0>0,α≥0,without smallness conditions on initial data.