Nous considérons un modèle provenant de la biologie, composé dʼéquations de chimiotactisme couplées aux équations de fluide visqueux incompressible par le transport et le forçage externe. Lʼexistence globale des solutions du problème de Cauchy est étudiée sous certaines conditions. Précisément, pour le système chimiotactisme–Navier–Stokes en deux dimensions dʼespace, nous obtenons lʼexistence globale pour des données grandes. En trois dimensions dʼespace, nous démontrons lʼexistence globale des solutions faibles pour le système chimiotactisme–Stokes avec une diffusion non-linéaire de la densité des cellules.
We consider a model arising from biology, consisting of chemotaxis equations coupled to viscous incompressible fluid equations through transport and external forcing. Global existence of solutions to the Cauchy problem is investigated under certain conditions. Precisely, for the chemotaxis–Navier–Stokes system in two space dimensions, we obtain global existence for large data. In three space dimensions, we prove global existence of weak solutions for the chemotaxis–Stokes system with nonlinear diffusion for the cell density.
@article{AIHPC_2011__28_5_643_0, author = {Liu, Jian-Guo and Lorz, Alexander}, title = {A coupled chemotaxis-fluid model: {Global} existence}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {643--652}, publisher = {Elsevier}, volume = {28}, number = {5}, year = {2011}, doi = {10.1016/j.anihpc.2011.04.005}, mrnumber = {2838394}, zbl = {1236.92013}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2011.04.005/} }
TY - JOUR AU - Liu, Jian-Guo AU - Lorz, Alexander TI - A coupled chemotaxis-fluid model: Global existence JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 643 EP - 652 VL - 28 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2011.04.005/ DO - 10.1016/j.anihpc.2011.04.005 LA - en ID - AIHPC_2011__28_5_643_0 ER -
%0 Journal Article %A Liu, Jian-Guo %A Lorz, Alexander %T A coupled chemotaxis-fluid model: Global existence %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 643-652 %V 28 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2011.04.005/ %R 10.1016/j.anihpc.2011.04.005 %G en %F AIHPC_2011__28_5_643_0
Liu, Jian-Guo; Lorz, Alexander. A coupled chemotaxis-fluid model: Global existence. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 5, pp. 643-652. doi : 10.1016/j.anihpc.2011.04.005. http://www.numdam.org/articles/10.1016/j.anihpc.2011.04.005/
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