Global weak solutions to a 3-dimensional degenerate and singular chemotaxis-Navier-Stokes system with logistic source

This paper considers the degenerate and singular chemotaxis-Navier-Stokes system with logistic term {n(t) + u center dot del n = Delta n(m) - chi del center dot (n del c) + kappa n - mu n(2) , x epsilon Omega, t > 0, c(t) + u center dot del c = Delta c - nc, x epsilon Omega, t > 0, u(t) + (u center dot del)u = Delta u + del P + n del Phi, del center dot u = 0, x epsilon Omega, t > 0, where Omega subset of R-3 is a bounded domain and chi, kappa >= 0 and m, mu > 0. In the above system without fluid environment Jin (2017) showed existence and boundedness of global weak solutions. On the other hand, in the above system with m = 1, Lankeit (2016) established global existence of weak solutions. However, the above system with m > 0 has not been studied yet. The purpose of this talk is to establish global existence of weak solutions in the chemotaxis-Navier-Stokes system with degenerate diffusion and logistic term. (C) 2018 Elsevier Ltd. All rights reserved.