UPPER BOUNDS FOR THE BLOW-UP TIME OF THE 2-D PARABOLIC-ELLIPTIC PATLAK-KELLER-SEGEL MODEL OF CHEMOTAXIS - CNRS - Centre national de la recherche scientifique Access content directly
Preprints, Working Papers, ... Year : 2023

UPPER BOUNDS FOR THE BLOW-UP TIME OF THE 2-D PARABOLIC-ELLIPTIC PATLAK-KELLER-SEGEL MODEL OF CHEMOTAXIS

Patrick Maheux
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Abstract

In this paper, we obtain upper bounds for the critical time T * of the blowup for the parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. Such estimates is rarely obtained and discuss in the papers on the subject No moment condition or/and entropy condition are required on the initial data; only the usual assumptions of non-negativity and finiteness of the mass is assumed. The result is expressed not only in terms of the supercritical mass M > 8π, but also in terms of the shape of the initial data.
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hal-04139369 , version 1 (23-06-2023)

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Patrick Maheux. UPPER BOUNDS FOR THE BLOW-UP TIME OF THE 2-D PARABOLIC-ELLIPTIC PATLAK-KELLER-SEGEL MODEL OF CHEMOTAXIS. 2023. ⟨hal-04139369⟩
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