ASYMPTOTIC BEHAVIORS OF SOLUTIONS FOR AN AEROTAXIS MODEL COUPLED TO FLUID EQUATIONS

被引:22
作者
Chae, Myeongju [1 ]
Kang, Kyungkeun [2 ]
Lee, Jihoon [3 ]
机构
[1] Hankyong Natl Univ, Dept Appl Math, Ansung 456749, South Korea
[2] Yonsei Univ, Dept Math, Seoul 03722, South Korea
[3] Chung Ang Univ, Dept Math, Seoul 06974, South Korea
关键词
GLOBAL EXISTENCE; SYSTEM; DECAY;
D O I
10.4134/JKMS.2016.53.1.127
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a coupled system of Keller-Segel type equations and the incompressible Navier-Stokes equations in spatial dimension two. We show temporal decay estimates of solutions with small initial data and obtain their asymptotic profiles as time tends to infinity.
引用
收藏
页码:127 / 146
页数:20
相关论文
共 28 条
[1]  
[Anonymous], 2003, DMV
[2]   Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier-Stokes equation [J].
Carlen, EA ;
Loss, M .
DUKE MATHEMATICAL JOURNAL, 1995, 81 (01) :135-157
[3]   ASYMPTOTIC-BEHAVIOR FOR THE VORTICITY EQUATIONS IN DIMENSIONS 2 AND 3 [J].
CARPIO, A .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1994, 19 (5-6) :827-872
[4]   Global Existence and Temporal Decay in Keller-Segel Models Coupled to Fluid Equations [J].
Chae, Myeongju ;
Kang, Kyungkeun ;
Lee, Jihoon .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2014, 39 (07) :1205-1235
[5]   EXISTENCE OF SMOOTH SOLUTIONS TO COUPLED CHEMOTAXIS-FLUID EQUATIONS [J].
Chae, Myeongju ;
Kang, Kyungkeun ;
Lee, Jihoon .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (06) :2271-2297
[6]   Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach [J].
Chertock, A. ;
Fellner, K. ;
Kurganov, A. ;
Lorz, A. ;
Markowich, P. A. .
JOURNAL OF FLUID MECHANICS, 2012, 694 :155-190
[7]   GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR A KELLER-SEGEL-FLUID MODEL WITH NONLINEAR DIFFUSION [J].
Chung, Yun-Sung ;
Kang, Kyungkeun ;
Kim, Jaewoo .
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 51 (03) :635-654
[8]   CHEMOTAXIS-FLUID COUPLED MODEL FOR SWIMMING BACTERIA WITH NONLINEAR DIFFUSION: GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR [J].
Di Francesco, Marco ;
Lorz, Alexander ;
Markowich, Peter A. .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 28 (04) :1437-1453
[9]   Global Solutions to the Coupled Chemotaxis-Fluid Equations [J].
Duan, Renjun ;
Lorz, Alexander ;
Markowich, Peter .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (09) :1635-1673
[10]   Global stability of vortex solutions of the two-dimensional Navier-Stokes equation [J].
Gallay, T ;
Wayne, CE .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005, 255 (01) :97-129