Open Access
2016 Global regularity of chemotaxis equations with advection
Saad Khan, Jay Johnson, Elliot Cartee, Yao Yao
Involve 9(1): 119-131 (2016). DOI: 10.2140/involve.2016.9.119


We study the Patlak–Keller–Segel (PKS) equations in 2D that describe chemotaxis with an additional advection term. We show that solutions are globally regular for smooth initial data with subcritical mass as long as the flow has nonpositive divergence. For initial data with supercritical mass, numerical simulations suggest that blow-up might be prevented by imposing some strong incompressible advection term.


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Saad Khan. Jay Johnson. Elliot Cartee. Yao Yao. "Global regularity of chemotaxis equations with advection." Involve 9 (1) 119 - 131, 2016.


Received: 25 August 2014; Revised: 8 January 2015; Accepted: 9 January 2015; Published: 2016
First available in Project Euclid: 22 November 2017

zbMATH: 1332.35059
MathSciNet: MR3438449
Digital Object Identifier: 10.2140/involve.2016.9.119

Primary: 35A01

Keywords: advection , chemotaxis , Keller–Segel , partial differential equations , PDE , symmetric decreasing rearrangement

Rights: Copyright © 2016 Mathematical Sciences Publishers

Vol.9 • No. 1 • 2016
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