Global well-posedness of Chemotaxis-Navier–Stokes system with refined rough initial data in [formula omitted

Abstract

We consider the global solvability of the incompressible Chemotaxis-Navier–Stokes system in Rd,d=2,3. We first investigate the global well-posedness of Chemotaxis-Navier–Stokes equations in R2 by involving a double exponential function of the initial velocity field u0 and the initial chemical concentration c0. By only giving the smallness assumption of initial cell density n0 and the horizontal components of velocity field u0h=(u01,u02) in critical Besov spaces, the global existence and uniqueness of the solution for Chemotaxis-Navier–Stokes equations in R3 is also established. The main contribution of this paper is to supply an improved assumption on initial data and remove the smallness condition on initial chemical concentration c0 in both dimensional two and three.