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SUMMARY:Keller-Segel\, fast-diffusion\, and functional inequalities - Jos
 é Antonio Carrillo de la Plata (Universitat Autònoma de Barcelona)
DTSTART:20120208T150000Z
DTEND:20120208T160000Z
UID:TALK35792@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:We will show how the critical mass classical Keller-Segel syst
 em and the critical displacement convex fast-diffusion equation in two dim
 ensions are related. On one hand\, the critical fast diffusion entropy fun
 ctional helps to show global existence around equilibrium states of the cr
 itical mass Keller-Segel system. On the other hand\, the critical fast dif
 fusion flow allows to show functional inequalities such as the Logarithmic
  HLS inequality in simple terms who is essential in the behavior of the su
 bcritical mass Keller-Segel system. HLS inequalities can also be recovered
  in several dimensions using this procedure. It is crucial the relation to
  the GNS inequalities obtained by DelPino and Dolbeault. This talk corresp
 onds to two works in collaboration with E. Carlen and A. Blanchet\, and wi
 th E. Carlen and M. Loss.
LOCATION:MR9\, CMS
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