dc.contributor |
Centre de Recerca Matemàtica |
dc.contributor.author |
Blanchet, Adrien |
dc.contributor.author |
Carrillo, José A. |
dc.contributor.author |
Masmoudi, Nader |
dc.date.accessioned |
2007-06-25T14:04:00Z |
dc.date.available |
2007-06-25T14:04:00Z |
dc.date.created |
2007-01 |
dc.date.issued |
2007-01 |
dc.identifier.uri |
http://hdl.handle.net/2072/4225 |
dc.format.extent |
30 |
dc.format.extent |
318820 bytes |
dc.format.mimetype |
application/pdf |
dc.language.iso |
eng |
dc.publisher |
Centre de Recerca Matemàtica |
dc.relation.ispartofseries |
Prepublicacions del Centre de Recerca Matemàtica;734 |
dc.rights |
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/) |
dc.subject.other |
Equacions diferencials |
dc.subject.other |
Geometria projectiva |
dc.title |
Infinite time aggregation for the critical Patlak-Keller-Segel model in R2 |
dc.type |
info:eu-repo/semantics/preprint |
dc.subject.udc |
517 - Anàlisi |
dc.subject.udc |
514 - Geometria |
dc.description.abstract |
We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates.
We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the
critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded. |