Solvability of an attraction-repulsion chemotaxis Navier-Stokes system with arbitrary porous medium diffusion

Abstract

In this work, we proposed a model that describes the influence of two chemically opposed stimuli in the movement of species living in a fluid environment. We investigated the well-posedness of a system that models the attraction-repulsion chemotaxis Navier-Stokes system with nonlinear diffusion. We validate the existence of a global three-dimensional weak solution. Furthermore, with some restrictions on the nonlinear exponent and degradation coefficients of the chemical signal, we established the existence of a three-dimensional global bounded weak solutions for the system. For more information see https://ejde.math.txstate.edu/Volumes/2024/75/abstr.html