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Critical Keller-Segel meets Burgers on S1 : Large-time smooth solutions

Abstract: We show that solutions to the parabolic?elliptic Keller?Segel system on S1 with critical fractional diffusion (-?) 1/2remain smooth for any initial data and any positive time. This disproves, at least in the periodic setting, the large-data-blowup conjecture by Bournaveas and Calvez [15]. As a tool, we show smoothness of solutions to a modified critical Burgers equation via a generalization of the ingenious method of moduli of continuity by Kiselev, Nazarov and Shterenberg [35] over a setting where the considered equation has no scaling. This auxiliary result may be interesting by itself. Finally, we study the asymptotic behavior of global solutions corresponding to small initial data, improving the existing results. © 2016 IOP Publishing Ltd & London Mathematical Society.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Nonlinearity 29 (2016) 3810-3836

Editorial: Institute of Physics

 Fecha de publicación: 01/10/2016

Nº de páginas: 27

Tipo de publicación: Artículo de Revista

 DOI: 10.1088/0951-7715/29/12/3810

ISSN: 0951-7715,1361-6544

Url de la publicación: https://doi.org/10.1088/0951-7715/29/12/3810

Autores/as