School of Mathematical Sciences
Fudan University
220 Handan Road
Shanghai 200433, China
email: jpyang22@m.fudan.edu.cn
Jiaping Yang
Abstract:
We study concentration expansions for the two-dimensional Keller-Segel free energy.
The main result concerns semi-discrete quadratic optimal transport interpolations
from a bounded compactly supported density to a prescribed finite atomic measure.
Along these paths the energy admits a logarithmic expansion whose leading coefficient
depends only on the masses assigned to the atoms. This coefficient captures the
entropy-attraction balance associated with a prescribed finite splitting of the mass.
Partial-concentration families with a diffuse remainder are analyzed by the same method.
We also quantify how prescribed packet merging changes the leading coefficient, analyze
critical profile relaxation and mesoscopic center coalescence, and construct explicit one-step JKO competitors.
Submitted May 20, 2026. Published October 6, 2026.
Math Subject Classifications: 35K55, 35Q92, 49Q22.
Key Words: Keller-Segel equation; critical mass; Wasserstein distance; JKO scheme; semi-discrete optimal transport.
DOI: 10.58997/ejde.2026.79
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Jiaping Yang School of Mathematical Sciences Fudan University 220 Handan Road Shanghai 200433, China email: jpyang22@m.fudan.edu.cn |
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