A coupled anisotropic chemotaxis-fluid model: The case of two-sidedly degenerate diffusion

被引：13
作者：
Chamoun, Georges [1 ,2 ,3 ]
Saad, Mazen [1 ]
Talhouk, Raafat [2 ,3 ]
机构：
[1] Ecole Cent Nantes, UMR CNRS 6629, Lab Math Jean Leray, F-44321 Nantes, France
[2] Univ Libanaise, EDST, Hadath, Beyrouth, Lebanon
[3] Fac Sci I, Math Lab, Hadath, Beyrouth, Lebanon
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2014年 / 68卷 / 09期
关键词：
Degenerate parabolic equation; Navier-Stokes equations; Heterogeneous and anisotropic diffusion; Global existence of solutions; GLOBAL EXISTENCE;
D O I：
10.1016/j.camwa.2014.04.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, the mathematical analysis of a model arising from biology consisting of diffusion, chemotaxis with volume filling effect and transport through an incompressible fluid, is studied. Motivated by numerical and modeling issues, the global-in-time existence of weak solutions to this model is investigated. The novelty with respect to other related papers lies in the presence of two-sidedly nonlinear degenerate diffusion and of anisotropic and heterogeneous diffusion tensors where we prove the global existence for a Chemotaxis-Navier-Stokes system in space dimensions less than or equal to four and we show the uniqueness of weak solutions for the Chemotaxis-Stokes system in two or three space dimensions under further assumptions. (C) 2014 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1052 / 1070
页数：19
相关论文
共 23 条
  • [1] [Anonymous], 1968, LINEAR QUASILINEAR E
  • [2] On a two-sidedly degenerate chemotaxis model with volume-filling effect
    Bendahmane, Mostafa
    Karlsen, Kenneth H.
    Urbano, Jose Miguel
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2007, 17 (05) : 783 - 804
  • [3] Boyer F., 2003, DEA MATH APPL CALCUL
  • [4] Brezis H., 1983, Analyse fonctionnelle, Theorie et applications
  • [5] Chamoun G., 2013, J NMPDE
  • [6] Chamoun G., 2013, J BIOMATH, V2
  • [7] Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach
    Chertock, A.
    Fellner, K.
    Kurganov, A.
    Lorz, A.
    Markowich, P. A.
    [J]. JOURNAL OF FLUID MECHANICS, 2012, 694 : 155 - 190
  • [8] CHEMOTAXIS-FLUID COUPLED MODEL FOR SWIMMING BACTERIA WITH NONLINEAR DIFFUSION: GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR
    Di Francesco, Marco
    Lorz, Alexander
    Markowich, Peter A.
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2010, 28 (04) : 1437 - 1453
  • [9] Global Solutions to the Coupled Chemotaxis-Fluid Equations
    Duan, Renjun
    Lorz, Alexander
    Markowich, Peter
    [J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2010, 35 (09) : 1635 - 1673
  • [10] Global existence for a parabolic chemotaxis model with prevention of overcrowding
    Hillen, T
    Painter, K
    [J]. ADVANCES IN APPLIED MATHEMATICS, 2001, 26 (04) : 280 - 301
123