| 赵继红,蔡中博,罗永轲.三维趋化流体耦合系统整体解的最优衰减估计 *[J].数学年刊A辑,2022,43(1):17~36 |
| 三维趋化流体耦合系统整体解的最优衰减估计 * |
| Optimal Decay Estimates of Global Solutions for the 3D Coupled Chemotaxis-Fluid System |
| Received:December 04, 2020 Revised:October 25, 2021 |
| DOI：10.16205/j.cnki.cama.2022.0002 |
| 中文关键词: 趋化流体模型, Keller–Segel 方程, Navier–Stokes 方程组, 衰减, Besov 空间 |
| 英文关键词:Chemotaxis-fluid model, Keller– Segel equations, Navier– Stokes e-quations, Decay, Besov spaces |
| 基金项目:国家自然科学基金 (No. 11961030), 陕西省自然科学基金 (No. 2022JM-034) 和宝鸡文理学院人才 引进项目 (No. 209040020) |
| Author Name | Affiliation | | ZHAO Jihong | School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China. | | CAI Zhongbo | School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China. | | LUO Yongke | School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China. |
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| 中文摘要: |
| 本文主要研究一类由抛物 - 抛物型 Keller–Segel 方程组和粘性不可压 Navier–Stokes 方程组 鹅合而成的三维非线性耗散系统. 利用 Bony 微局部分析和 Besov 空间插值理论, 作者建立了该系统 在临界 Besov 空间中小初值问题整体解的最优衰减估计, 将 [Zhao J H, Zhou J J. Temporal decay in negative Besov spaces for the 3D coupled chemotaxis-?uid equations [J]. Nonlinear Analysis: Real World Applications, 2018, 42:160– 179.] 中的衰减结果的可积性指标推广至了更一般的情形. |
| 英文摘要: |
| In this paper, the authors are concerned with a nonlinear dissipative system coupling the parabolic-parabolic Keller– Segel system to the viscous incompressible Navier– Stokes equations in spatial dimensions three. The decay estimates of global solutions were established for small initial data in critical Besov spaces with minimal regularity indices by using the Bony’s paradi?erential calculus and the interpolation inequalities in Besov spaces, which extends the integrable indices of decay results in [Zhao, J. H. and Zhou, J. J., Temporal decay in negative Besov spaces for the 3D coupled chemotaxis-?uid equations, Nonlinear Analysis: Real World Applications, 2018, vol. 42, pp. 160– 179.] to a more broader cases. |
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