Refined Hyper-Contractivity and Uniqueness for a Two-Species Chemotaxis Model with Two Chemicals in $\mathbb{R}^{2}$
Received:November 24, 2025  Revised:February 26, 2026
Key Words: Bessel potential   refined hyper-contractivity   semigroup theory   uniqueness  
Fund Project:the National Natural Science Foundation of China (Grant No.12171218) and the Natural Science Foundation Program of Liaoning Province (Grant No.2024-MS-002).
Author NameAffiliation
Li Shuhuan School of Mathematics and Statistics, Liaoning University, Shenyang, Liaoning 110036, P. R. China 
Wang Jinhuan School of Mathematics and Statistics, Liaoning University, Shenyang, Liaoning 110036, P. R. China 
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Citation:
DOI:10.3770/j.issn:2095-2651.2026.04.006
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