On a chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics: Theoretical and numerical analysis

Abstract

This work is devoted to the theoretical and numerical analysis of a two-species chemotaxis-Navier-Stokes system with Lotka-Volterra competitive kinetics in a bounded domain of Rd, d=2,3. First, we study the existence of global weak solutions and establish a regularity criterion which provides sufficient conditions to ensure the strong regularity of the weak solutions. After, we propose a finite element numerical scheme approximating the continuous model, for which we study the well-posedness and derive some uniform estimates for the discrete variables. We present a convergence analysis proving optimal error estimates and show some numerical simulations in agreement with our theoretical analysis and theoretical results reported in previous works.