Electron. J. Differential Equations, Vol. 2024 (2024), No. 75, pp. 1-28.

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

Yadhavan Karuppusamy, Shangerganesh Lingeshwaran, Manimaran Jeyaraj

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.
DOI: 10.58997/ejde.2024.75

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Yadhavan Karuppusamy
Department of Applied Sciences
National Institute of Technology Goa
Cuncolim - 403 703, Goa, India
email: yadhavan@nitgoa.ac.in
Shangerganesh Lingeshwaran
Department of Applied Sciences
National Institute of Technology Goa
Cuncolim - 403 703, Goa, India
email: shangerganesh@nitgoa.ac.in
Manimaran Jeyaraj
School of Advanced Sciences
Vellore Institute of Technology
Chennai- 600 127, Tamil Nadu, India
email: manimaran.j@vit.ac.in

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