Keller-Segel-Navier-Stokes systems involving general sensitivities with signal-dependent power-law decay

초록

This paper investigates a two-dimensional Keller–Segel–Navier–Stokes system with a tensor-valued chemotactic sensitivity S(x,n,c). Under a signal-dependent power-decay condition |S(x,n,c)|≤s0(s1+c)−γ, we establish the global existence and uniform-in-time boundedness of classical solutions for both fluid-coupled (γ>1/2) and fluid-free (γ>0) systems. The proof relies on a sequence of localized energy estimates, including the Lloc2-smallness of the weighted gradient of the signal concentration, to overcome the mathematical difficulties arising from signal production and fluid transport. Furthermore, under specific structural assumptions on the sensitivity tensor, we prove that solutions of the fluid-free system converge exponentially to the spatially homogeneous steady state. To this end, we establish an interpolation inequality involving the Hölder norm, which is of independent interest and seems to have broad applications. © 2026 Elsevier Inc.

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