Global well-posedness for the two-dimensional coupled chemotaxis-generalized Navier-Stokes system with logistic growth

In this paper, we investigate Cauchy problem for the two-dimensional incompressible chemotaxisNavier-Stokes equations with the lower fractional diffusion {partial derivative(t)n + u . del n - Delta n = -del . (n del c) + lambda n - mu n(2), partial derivative(t)c + u . del c - Delta c = -cn, partial derivative(t)u + u. del u + Lambda(2 alpha) u + del P = -n del phi, where Lambda := (-Delta)(1/2) and alpha is an element of [1/2, 1]. We obtain the global-in-time existence and uniqueness of weak solution to the equations for a class of large initial data by making use of the coupled structure of system and damping effect of the logistic source, and developing the L-4/3 (R-2) estimate for vorticity. (C) 2020 Elsevier Inc. All rights reserved.