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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (6): 84-91.doi: 10.6040/j.issn.1671-9352.0.2022.414

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一类趋化流体模型大解的整体存在性

蔡中博(),赵继红*()   

  1. 宝鸡文理学院数学与信息科学学院,陕西 宝鸡 721013
  • 收稿日期:2022-07-24 出版日期:2023-06-20 发布日期:2023-05-23
  • 通讯作者: 赵继红 E-mail:rebirthzbcai@163.com;jihzhao@163.com
  • 作者简介:蔡中博(1996—),男,硕士研究生,研究方向为偏微分方程. E-mail: rebirthzbcai@163.com
  • 基金资助:
    国家自然科学基金资助项目(11961030);陕西省自然科学基金资助项目(2022JM-034);陕西省教育厅自然科学专项科研计划项目(21JK0479);宝鸡文理学院研究生创新项目(YJSCX22YB28)

Global existence of large solutions for a class of chemotaxis-fluid model

Zhongbo CAI(),Jihong ZHAO*()   

  1. School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China
  • Received:2022-07-24 Online:2023-06-20 Published:2023-05-23
  • Contact: Jihong ZHAO E-mail:rebirthzbcai@163.com;jihzhao@163.com

摘要:

主要研究了一类由抛物-抛物型Keller-Segel方程组与不可压Navier-Stokes方程组耦合而成的趋化流体模型。利用加权Chemin-Lerner范数、Besov空间插值理论和Fourier微局部分析,建立了该模型在临界Besov空间中一类大解的整体存在性。

关键词: 趋化流体模型, 大解, 整体存在性, Besov空间

Abstract:

In this paper, we are concerned with a class of chemotaxis-fluid models, which is a coupled system by parabolic-parabolic Keller-Segel equations and incompressible Navier-Stokes equations. Making full use of the weighted Chemin-Lerner type norm, the interpolation theory in Besov spaces and Fourier localization technique, the global existence of large solutions is obtained in critical Besov spaces.

Key words: chemotaxis-fluid model, large solution, global existence, Besov space

中图分类号: 

  • O175.21
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