Verão ICMC 2025

Existence of weak solutions for a nonhomogeneous incompressible cell-fluid Navier-Stokes model with chemotaxis

Juliana Honda Lopes

Abstract

This work is concerned with the mathematical analysis of a gen- eral cell-fluid Navier-Stokes model with the inclusion of chemotaxis proposed by [2]. This general model relays on a mixture theory multi- phase formulation. It consists of two mass balance equations and two general momentum balance equations, respectively, for the cell and fluid phase, combined with a convection-diffusion-reaction equation for oxygen. We investigate the existence of weak solutions in a two or three-dimensional bounded domain when the fluids are assumed to be incompressible with constant volume fraction.

JHL was financed by FAPESP-Brazil grant 2020/14206-3.

References

[1] J. H. Lopes, G. Planas, Existence of weak solutions for a nonhomo- geneous incompressible cell-fluid Navier-Stokes model with chemotaxis, Math. Methods Appl. Sci. 46 13695-13715 (2023).

[2] Y. Qiao, S. Evje, A general cell-fluid Navier-Stokes model with inclu- sion of chemotaxis, Math. Models Methods Appl. Sci. 30 (6) 1167-1215 (2020).