• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Uniqueness and long time asymptotic for the parabolic-parabolic Keller-Segel equation

Thumbnail
Date
2017
Publisher city
Paris
Link to item file
https://hal.archives-ouvertes.fr/hal-01011361
Dewey
Analyse
Sujet
Keller-Segel system; long-time behavior; stability; regularization; uniqueness; self-similar variables
Journal issue
Communications in Partial Differential Equations
Volume
42
Number
2
Publication date
2017
Article pages
291-345
Publisher
Marcel Dekker
DOI
http://dx.doi.org/10.1080/03605302.2017.1280682
URI
https://basepub.dauphine.fr/handle/123456789/11967
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Carrapatoso, Kleber
Mischler, Stéphane
Type
Article accepté pour publication ou publié
Abstract (EN)
The present paper deals with the parabolic-parabolic Keller-Segel equation in the plane inthe general framework of weak (or ``free energy") solutions associated to an initial datum with finite mass M<8π, finite second log-moment and finite entropy. The aim of the paper is twofold:(1) We prove the uniqueness of the ``free energy" solution. The proof uses a DiPerna-Lions renormalizing argument which makes possible to get the ``optimal regularity" as well as an estimate of the difference of two possible solutions in the critical L4/3 Lebesgue norm similarly as for the 2d vorticity Navier-Stokes equation. (2) We prove a radially symmetric and polynomial weighted L2 exponential stability of the self-similar profile in the quasi parabolic-elliptic regime. The proof is based on a perturbation argument which takes advantage of the exponential stability of the self-similar profile for the parabolic-elliptic Keller-Segel equation established in \cite{CamposDolbeault2012,EM}.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.