Well‐Posedness and Long‐Time Behavior for Evolutionary Bioconvective Flow Equations With Brinkman‐Forchheimer Damping in Three‐Dimensional Porous Biological Media

ABSTRACT 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.