Mathematical modeling demonstrates global existence, uniqueness, and long-term decay in 3D bioconvective flow, suggesting predictable limits on bacterial infection propagation in porous tissues.
We study a bioconvective flow model in a porous medium with a Brinkman‐Forchheimer nonlinear damping term. Such a model arises naturally in biomedical applications, including bacterial transport in tissues, infection propagation, and biofluid dynamics in porous biological structures. We prove the global‐in‐time existence of weak solutions. Under suitable assumptions on the Forchheimer exponent and the initial microorganism concentration, the solution depends continuously on the initial data and is therefore unique. Moreover, for a range of parameters, we obtain uniform‐in‐time bounds for the velocity and the concentration and show that the concentration vanishes as time tends to infinity.
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Châabani et al. (2026) studied this question.
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