Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 75, pp. 1-28.

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

Authors: Yadhavan Karuppusamy (National Institute of Tech, Goa, India)
         Shangerganesh Lingeshwaran (National Institute of Tech, Goa, India)
         Manimaran Jeyaraj (Vellore Institute of Tech, Tamil Nadu, India)
  
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.

Submitted May 24, 2024. Published November 25, 2024.
Math Subject Classifications: 35Q30, 35K57, 35D30, 92C17.
Key Words: Attraction-repulsion; chemotaxis; Navier-Stokes; weak solution.