Decay estimate of solutions to the coupled chemotaxis-fluid equations in R3

被引:17
作者
Tan, Zhong [1 ,2 ]
Zhou, Jianfeng [1 ]
机构
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[2] Xiamen Univ, Fujian Prov Key Lab Math Modeling & Sci Comp, Xiamen 361005, Peoples R China
基金
中国国家自然科学基金;
关键词
Chemotaxis-Navier Stokes equations; Global existence; Time decay rate; Energy method; Homogeneous Sobolev space; Homogeneous Besov space; KELLER-SEGEL SYSTEM; GLOBAL EXISTENCE; WEAK SOLUTIONS; STOKES MODEL; RATES;
D O I
10.1016/j.nonrwa.2018.01.006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We are concerned with a model arising from biology, which is coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and external forcing. We study the large time behavior of solutions near a constant states to the chemotaxis-Navier-Stokes system in R-3. Appealing to a pure energy method, we first obtain a global existence theorem by assuming that the H-3 norm of the initial data is small, but the higher order derivatives can be arbitrary large. If the initial data belongs to homogeneous Sobolev norms H-s (0 <= s < 3/2 or homogeneous Besov norms B-2,infinity(-s) (0 < s <= 3/2), we obtain the optimal decay rates of the solutions and its higher order derivatives. As an immediate byproduct, we also obtain the usual L-P - L-2 (1 <= p <= 2) type of the decay rates without requiring that the L-P norm of initial data is small. (C) 2018 Elsevier Ltd. All rights reserved.
引用
收藏
页码:323 / 347
页数:25
相关论文
共 50 条
[31]   Uniform Lp Estimates for Solutions to the Inhomogeneous 2D Navier-Stokes Equations and Application to a Chemotaxis-Fluid System with Local Sensing [J].
Fuest, Mario ;
Winkler, Michael .
JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2024, 26 (04)
[32]   DECAY ESTIMATES OF THE NON-ISENTROPIC COMPRESSIBLE FLUID MODELS OF KORTEWEG TYPE IN R3 [J].
Zhang, Xu ;
Tan, Zhong .
COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2014, 12 (08) :1437-1456
[33]   Global existence and time decay rates of the two-phase fluid system in R3 [J].
Zhang, Yinghui ;
Wang, Juan ;
Xiao, Changguo ;
Ma, Lintao .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 72 (05)
[34]   Global existence and asymptotic behavior of solutions to a chemotaxis-fluid system on general bounded domains [J].
Jiang, Jie ;
Wu, Hao ;
Zheng, Songmu .
ASYMPTOTIC ANALYSIS, 2015, 92 (3-4) :249-258
[35]   Upper bound of decay rate for solutions to the Navier-Stokes-Voigt equations in R3 [J].
Zhao, Caidi ;
Zhu, Hongjin .
APPLIED MATHEMATICS AND COMPUTATION, 2015, 256 :183-191
[36]   Martingale solutions of the stochastic Hall-magnetohydrodynamics equations on R3 [J].
Motyl, Elzbieta .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 362 :514-575
[37]   Decay characterization of solutions to generalized Hall-MHD system in R3 [J].
Zhao, Xiaopeng ;
Zhu, Mingxuan .
JOURNAL OF MATHEMATICAL PHYSICS, 2018, 59 (07)
[38]   THE TIME DECAY RATES OF THE CLASSICAL SOLUTION TO THE POISSON-NERNST-PLANCK-FOURIER EQUATIONS IN R3 [J].
Tong, Leilei ;
Tan, Zhong ;
Zhang, Xu .
ACTA MATHEMATICA SCIENTIA, 2022, 42 (03) :1081-1102
[39]   DECAY ESTIMATES OF SOLUTIONS TO THE COMPRESSIBLE NAVIER STOKES MAXWELL SYSTEM IN R3 [J].
Tan, Zhong ;
Tong, Leilei .
COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2016, 14 (05) :1189-1212
[40]   Global Solvability to a 3D Chemotaxis-Fluid Model with Matrix-Valued Supercritical Sensitivities [J].
Xu, Wei ;
Sun, Tao .
ACTA APPLICANDAE MATHEMATICAE, 2021, 173 (01)