Smoothness of critical, fractional Keller-Segel and Burgers equations in 1d

Speaker(s)

Jan Burczak

Date

May 21, 2015, 12:30 p.m.

Room

room 4060

Seminar

Seminar of Mathematical Physics Equations Group

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I will present a disproof of a blowup conjecture for the critical, fractional one-dimensional Keller-Segel system. The main tool is a smoothness result for a modified Burgers system; it follows from a modification of the famous method of moduli of continuity by Kiselev, Nazarov, Shterenberg and Volberg. If time permits, I will also present certain regularity results for Keller-Segel system with supercritical fractional diffusion. The talk is based on a joint work with Rafael Granero (Davies).

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