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Abstract We consider absorbing chemical reactions in a fluid flow modelled by the coupled advection–reaction–diffusion equations. In these systems, the interplay between chemical diffusion and fluid transportation causes the enhanced dissipation phenomenon. We show that the enhanced dissipation time scale, together with the reaction coupling strength, determines the characteristic time scale of the reaction.more » « less
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We study two types of divergence-free fluid flows on unbounded domains in two and three dimensions—hyperbolic and shear flows—and their influence on chemotaxis and combustion. We show that fast spreading by these flows, when they are strong enough, can suppress growth of solutions to PDE modeling these phenomena. This includes prevention of singularity formation and global regularity of solutions to advective Patlak-Keller-Segel equations on R 2 \mathbb {R}^2 and R 3 \mathbb {R}^3 , confirming numerical observations by Khan, Johnson, Cartee, and Yao [Involve 9 (2016), pp. 119–131], as well as quenching in advection-reaction-diffusion equations.more » « less
