JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 84-91.doi: 10.6040/j.issn.1671-9352.0.2022.414

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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

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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

CLC Number: 

  • O175.21
1 TUVAL I , CISNEROS L , DOMBROWSKI C , et al. Bacterial swimming and oxygen transport near contact lines[J]. Proceedings of the National Academy of Sciences, 2005, 102 (7): 2277- 2282.
doi: 10.1073/pnas.0406724102
2 LORZ A . Coupled chemotaxis fluid model[J]. Mathematical Models and Methods in Applied Sciences, 2010, 20 (6): 987- 1004.
doi: 10.1142/S0218202510004507
3 DUAN Renjun , LORZ A , MARKOWICH P . Global solutions to the coupled chemotaxis-fluid equations[J]. Communications in Partial Differential Equations, 2010, 35 (9): 1635- 1673.
doi: 10.1080/03605302.2010.497199
4 CHAE M , KANG K , LEE J . Existence of smooth solutions to coupled chemotaxis-fluid equations[J]. Discrete Continuous Dynamical Systems, 2013, 33 (6): 2271- 2297.
doi: 10.3934/dcds.2013.33.2271
5 ZHANG Qian . Local well-posedness for the chemotaxis-Navier-Stokes equations in Besov spaces[J]. Nonlinear Analysis: Real World Applications, 2014, 17, 89- 100.
doi: 10.1016/j.nonrwa.2013.10.008
6 HE Haibin , ZHANG Qian . Global existence of weak solutions for the 3D chemotaxis-Navier-Stokes equations[J]. Nonlinear Analysis: Real World Applications, 2017, 35, 336- 349.
doi: 10.1016/j.nonrwa.2016.11.006
7 ZHANG Qian , ZHENG Xiaoxin . Global well-posedness of axisymmetric solution to the 3D axisymmetric chemotaxis-Navier-Stokes equations with logistic source[J]. Journal of Differential Equations, 2021, 274, 576- 612.
doi: 10.1016/j.jde.2020.10.024
8 ZHANG Qian , ZHANG Yehua . Global well-posedness for the 3D incompressible Keller-Segel-Navier-Stokes equations[J]. Zeitschrift für Angewandte Mathematik und Physik, 2019, 70 (5): 1- 28.
9 CHOE H J , LKHAGVASUREN B , YANG M . Wellposedness of the Keller-Segel-Navier-Stokes equations in the critical Besov spaces[J]. Communications on Pure Applied Analysis, 2015, 14 (6): 2453- 2464.
doi: 10.3934/cpaa.2015.14.2453
10 ZHAO Jihong , ZHOU Jianjun . Temporal decay in negative Besov spaces for the 3D coupled chemotaxis-fluid equations[J]. Nonlinear Analysis: Real World Applications, 2018, 42, 160- 179.
doi: 10.1016/j.nonrwa.2018.01.001
11 ZHAO Jihong . Global existence in critical Besov spaces for the coupled chemotaxis-fluid equations[J]. Journal of Mathematical Analysis and Applications, 2018, 465 (2): 1010- 1024.
doi: 10.1016/j.jmaa.2018.05.041
12 YANG Minghua . Global solutions to Keller-Segel-Navier-Stokes equations with a class of large initial data in critical Besov spaces[J]. Mathematical Methods in the Applied Sciences, 2017, 40 (18): 7425- 7437.
doi: 10.1002/mma.4538
13 YANG Minghua , FU Zunwei , SUN Jinyi . Global solutions to chemotaxis-Navier-Stokes equations in critical Besov spaces[J]. Discrete Continuous Dynamical Systems-B, 2018, 23 (8): 3427- 3460.
doi: 10.3934/dcdsb.2018284
14 BONY J M . Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires[J]. Annales Scientifiques de l'école Normale Supérieure, 1981, 14 (2): 209- 246.
doi: 10.24033/asens.1404
15 BAHOURI H , CHEMIN J Y , DANCHIN R . Fourier analysis and nonlinear partial differential equations[M]. Berlin: Springer, 2011.
16 DANCHIN R . Local theory in critical spaces for compressible viscous and heat-conductive gases[J]. Communications in Partial Differential Equations, 2001, 26 (7-8): 1183- 1233.
doi: 10.1081/PDE-100106132
17 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.
ZHAO Jihong , CAI Zhongbo , LUO Yongke . Optimal decay estimates of global solutions for the 3D coupled chemotaxis-fluid system[J]. Chinese Annals of Mathematics: Series A, 2022, 43 (1): 17- 36.
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