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Title:
Suppression of Chemotactic Blow-up through Flows
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Abstract:
We study the advective-Patlak-Keller-Segel equations, which model chemotaxis phenomena of bacteria in a fluid stream. If the bacteria population is large and no fluid transportation is present, it is well-known that the solutions form Dirac-type singularities in finite time. We showed that strong hyperbolic or shear flows help suppress the blow-up of the equation on the plane or in the infinite channel. This result confirms the numerical observation made in Khan-Johnson-Cartee-Yao. This is joint work with Eitan Tadmor and Andrej Zlato\v{s}.
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