Global well-posedness of the 3D Patlak-Keller-Segel system near a straight line
Abstract
We consider the Cauchy problem of the three-dimensional parabolic-elliptic Patlak-Keller-Segel chemotactic model. The initial data is almost a Dirac measure supported on a straight line with mass less than 8π. We prove that if the data is sufficiently close to the straight line, then global well-posedness holds. This result is parallel to the work on vortex filament solutions of the Navier-Stokes equations by Bedrossian, Germain and Harrop-Griffiths filament.
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