کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4604334 1337434 2013 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Locally bounded global solutions in a three-dimensional chemotaxis-Stokes system with nonlinear diffusion
چکیده انگلیسی

This paper deals with a boundary-value problem in three-dimensional smoothly bounded domains for a coupled chemotaxis-Stokes system generalizing the prototype{nt+u⋅∇n=Δnm−∇⋅(n∇c),ct+u⋅∇c=Δc−nc,ut+∇P=Δu+n∇ϕ,∇⋅u=0, which describes the motion of oxygen-driven swimming bacteria in an incompressible fluid.It is proved that global weak solutions exist whenever m>87 and the initial data (n0,c0,u0)(n0,c0,u0) are sufficiently regular satisfying n0>0n0>0 and c0>0c0>0. This extends a recent result by Di Francesco, Lorz and Markowich [M. Di Francesco, A. Lorz, P.A. Markowich, Chemotaxis–fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior, Discrete Contin. Dyn. Syst. Ser. A 28 (2010) 1437–1453] which asserts global existence of weak solutions under the constraint m∈[7+21712,2].

RésuméCe papier considère un problème aux limites dans des domaines tridimensionnels réguliers et bornés, plus précisément, un système couplé de chemotaxie-Stokes qui généralise le prototype{nt+u⋅∇n=Δnm−∇⋅(n∇c),ct+u⋅∇c=Δc−nc,ut+∇P=Δu+n∇ϕ,∇⋅u=0 et qui décrit le mouvement des bactéries nageuses conduites par lʼoxygène dans un fluide incompressible.On montre que les solutions faibles globales existent quand m>87 et la donnée initiale (n0,c0,u0)(n0,c0,u0) est suffisamment régulière et vérifie n0>0n0>0 et c0>0c0>0. Cela étend le résultat récent de Di Francesco, Lorz et Markowich [M. Di Francesco, A. Lorz, P.A. Markowich, Chemotaxis–fluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior, Discrete Contin. Dyn. Syst. Ser. A 28 (2010) 1437–1453] qui affirme lʼexistence globale de solutions faibles sous la contrainte m∈[7+21712,2].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 30, Issue 1, January–February 2013, Pages 157–178
نویسندگان
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