Multi-point concentration expansions for the two-dimensional Keller-Segel free energy
- 1Fudan Univ., Shanghai, China
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.
Related
- Endpoint Energy Atoms Force Local Pressure Concentration in Three-Dimensional Navier-Stokes Flow
- Cavity collapse and kinetic energy concentration in three-dimensional free-boundary Euler flow
- Keller's conjecture for split finite-dimensional algebras
- Suppression of Blow-up in Two-dimensional Keller--Segel Systems by Stochastic Couette Flows
- Absence of critical mass phenomena in one-dimensional critical quasilinear Keller-Segel systems
BibTeX
@article{yang2026multipoint,
title = {{Multi-point concentration expansions for the two-dimensional Keller-Segel free energy}},
author = {Jiaping Yang},
journal = {Electronic Journal of Differential Equations},
year = {2026},
month = oct,
url = {http://ejde.math.txstate.edu/Volumes/2026/79/abstr.html},
note = {CC BY},
}
RIS
TY - JOUR
TI - Multi-point concentration expansions for the two-dimensional Keller-Segel free energy
AU - Jiaping Yang
PY - 2026
DA - 2026/10/23
JO - Electronic Journal of Differential Equations
UR - http://ejde.math.txstate.edu/Volumes/2026/79/abstr.html
AB - 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.
SN - 1072-6691
ER -