Investigates a chemotaxis-fluid system, revealing solution behavior for small initial conditions and implications for global existence and blow-up criteria.
The purpose of this paper is devoted to investigating a fractional parabolic‐elliptic chemotaxis system coupled with the Navier–Stokes equation in the whole space . We show the existence of a global mild solution to system (1.1) for small initial data in the scale invariant class demonstrating that and . Furthermore, by studying moments of lower order , we establish a blow‐up criterion of solution to system (1.1) with the help of the proof by contradiction.
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Jiang et al. (2026) studied this question.
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