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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.
Fuente: Nonlinearity, 2016, 29, 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
Proyecto español: MTM2014-59488-P
Url de la publicación: https://doi.org/10.1088/0951-7715/29/12/3810
Consultar en UCrea Leer publicación
BURCZAK, JAN
RAFAEL GRANERO BELINCHON
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