Boundedness and decay enforced by quadratic degradation in a three-dimensional chemotaxis–fluid system

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Global classical solutions in a two-dimensional chemotaxis-Navier-Stokes system with subcritical sensitivity (2018, background): “([50]), or on the construction of small-data solutions ([30], [4]), or also on systems involving logisitic growth restrictions as an additional dissipative mechanism ([13], [46]).”
A three-dimensional Keller–Segel–Navier–Stokes system with logistic source: Global weak solutions and asymptotic stabilization (2019, background): “1) have recently been shown to exist for any ρ ≥ 0, suitably good-natured f and appropriately large μ > 0 ([56]).”
Long-term behaviour in a chemotaxis-fluid system with logistic source (2016, methodology): “Chemotaxis fluid models including logistic growth (κ, μ > 0) have been treated in [38, 33, 36, 43, 4].”
Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation (2018, background): “1), inter alia accounting for nonlinear cell diffusion ([51], [6], [41], [55], [58]), for variants in the cross-diffusive interaction ([53], [20], [4], [39], [57]) or also in the signal evolution, or even containing couplings to further mechanisms and components such as haptotactic cues ([5], [40], ”