Existence of weak and regular solutions for Keller-Segel system with degradation coupled to fluid equations

Abstract

We establish the global well-posedness for the following chemotaxis-fluid system {partial derivative(t)n + u center dot del n = Delta n - del center dot(n del c) - mu n(q), partial derivative(t)c + u center dot del c = Delta c - c + n, partial derivative(t)u + kappa(u center dot del)u + del P = Delta u - n del phi, del center dot u = 0, in R-d, d = 2, 3, where mu > 0, q > 2-1/d and kappa is an element of {0, 1}. For either q >= 2, (kappa, d) = (1,2) or q > 2, (kappa, d) = (0, 3), we prove the global existence of regular solutions. In case that q > 2 - 1/d and kappa = 0, very weak solutions are constructed as well. (C) 2019 Elsevier Inc. All rights reserved.