Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1707576 | Applied Mathematics Letters | 2016 | 8 Pages |
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.
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Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Jian-Guo Liu, Jinhuan Wang,