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Global regularity
of chemotaxis equations with advection
Saad Khan, Jay Johnson, Elliot Cartee and Yao Yao
Vol. 9 (2016), No. 1, 119–131
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Abstract |
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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. |
Keywords
chemotaxis, partial differential equations, PDE, symmetric
decreasing rearrangement, advection, Keller–Segel
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Mathematical Subject Classification 2010
Primary: 35A01
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Milestones
Received: 25 August 2014
Revised: 8 January 2015
Accepted: 9 January 2015
Published: 17 December 2015
Communicated by Behrouz Emamizadeh
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Authors |
| Saad Khan | |
| Department of Mathematics New York University New York, NY 10012-1185 United States |
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| Jay Johnson | |
| Department of Mechanical
Engineering University of Texas at Austin Austin, TX 78712 United States |
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| Elliot Cartee | |
| Department of Mathematics Cornell University Ithaca, NY 14850 United States |
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| Yao Yao | |
| Department of Mathematics University of Wisconsin-Madison Madison, WI 53703 United States |
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