For the chemotaxis-Navier-Stokes system with porous medium diffusion, as m→∞ the solutions converge to a Hele-Shaw free boundary problem whose pressure satisfies the complementarity relation P∞(ΔP∞ − ∇·(χ(c∞)∇c∞))=0.
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Hele-Shaw limit of chemotaxis-Navier-Stokes flows
For the chemotaxis-Navier-Stokes system with porous medium diffusion, as m→∞ the solutions converge to a Hele-Shaw free boundary problem whose pressure satisfies the complementarity relation P∞(ΔP∞ − ∇·(χ(c∞)∇c∞))=0.