Global regularity of chemotaxis equations with advection
Abstract 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.
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.
Abstract
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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