Elsevier

Applied Mathematics Letters

Volume 52, February 2016, Pages 212-219
Applied Mathematics Letters

Refined hyper-contractivity and uniqueness for the Keller–Segel equations

https://doi.org/10.1016/j.aml.2015.09.001Get rights and content
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Abstract

This note considers the hyper-contractivity and the uniqueness of the weak solutions to the two dimensional Keller–Segel equations. We prove a refined hyper-contractive property and consequently obtain the uniqueness of global weak solutions provided that the initial data satisfy R2ρ0dx<8π, R2|x|ρ0dx< and R2ρ0logρ0dx<. We also extend the result to higher dimensions.

Keywords

Hyper-contractivity
Uniqueness
LlogL space
Semi-group theory

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