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The Keller–Segel–Navier–Stokes system    $$\begin{aligned} \left\{ \begin{array}{rcll} n_t + u\cdot \nabla n &amp;{}=&amp;{} \Delta n - \chi \nabla \cdot (n\nabla c) + \rho n-\mu n^2,\\ c_t + u\cdot \nabla c &amp;{}=&amp;{} \Delta c-c+n, \\ u_t + (u\cdot \nabla )u &amp;{}=&amp;{} \Delta u + \nabla P + n \nabla \phi + f(x,t), \qquad \nabla \cdot u=0, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$  n t + u · ∇ n = Δ n - χ ∇ · ( n ∇ c ) + ρ n - μ n 2 , c t + u · ∇ c = Δ c - c + n , u t + ( u · ∇ ) u = Δ u + ∇ P + n ∇ ϕ + f ( x , t ) , ∇ · u = 0 , ( ⋆ ) is considered in a smoothly bounded convex domain    $$\Omega \subset \mathbb {R}^3$$  Ω ⊂ R 3 , with    $$\phi \in W^{2,\infty }(\Omega )$$  ϕ ∈ W 2 , ∞ ( Ω ) and    $$f\in C^1(\bar{\Omega }\times [0,\infty );\mathbb {R}^3)$$  f ∈ C 1 ( Ω ¯ × [ 0 , ∞ ) ; R 3 ) , and with    $$\chi &gt;0, \rho \in \mathbb {R}$$  χ &gt; 0 , ρ ∈ R and    $$\mu &gt;0$$  μ &gt; 0 . As recent literature has shown, for all reasonably mild initial data a corresponding no-flux/no-flux/Dirichlet initial-boundary value problem possesses a global generalized solution, but the knowledge on its regularity properties has not yet exceeded some information on fairly basic integrability features. The present study reveals that whenever    $$\omega &gt;0$$  ω &gt; 0 , requiring that    $$\begin{aligned} \frac{\rho }{\min \{\mu ,\mu ^{\frac{3}{2}+\omega }\}} &lt; \eta \end{aligned}$$  ρ min { μ , μ 3 2 + ω } &lt; η with some    $$\eta =\eta (\omega )&gt;0$$  η = η ( ω ) &gt; 0 , and that  f  satisfies a suitable assumption on ultimate smallness, is sufficient to ensure that each of these generalized solutions becomes eventually smooth and classical. Furthermore, under these hypotheses (   $$\star $$  ⋆ ) is seen to admit an absorbing set with respect to the topology in    $$L^\infty (\Omega )$$  L ∞ ( Ω ) . By trivially applying to the case when    $$\mu &gt;0$$  μ &gt; 0 is arbitrary and    $$\rho \le 0$$  ρ ≤ 0 , these results especially assert essentially unconditional statements on eventual regularity in taxis-reaction systems interacting with liquid environments, such as arising in contexts of models for broadcast spawning discussed in recent literature.

Reaction-Driven Relaxation in Three-Dimensional Keller–Segel–Navier–Stokes Interaction