The parabolic-parabolic Keller-Segel model in $mathbb{R}^2$ - Mathematics > Analysis of PDEsReportar como inadecuado




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Abstract: This paper is devoted mainly to the global existence problem for thetwo-dimensional parabolic-parabolic Keller-Segel in the full space. We derive acritical mass threshold below which global existence is ensured. Usingcarefully energy methods and ad hoc functional inequalities we improve andextend previous results in this direction. The given threshold is supposed tobe the optimal criterion, but this question is still open. This globalexistence result is accompanied by a detailed discussion on the duality betweenthe Onofri and the logarithmic Hardy-Littlewood-Sobolev inequalities thatunderlie the following approach.



Autor: Vincent Calvez, Lucilla Corrias

Fuente: https://arxiv.org/







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