A coupled chemotaxis-fluid model: Global existence
Jian-Guo Liu,Alexander Lorz +1 more
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In this paper, the authors considered a model arising from biology, consisting of chemotaxis equations coupled to viscous incompressible fluid equations through transport and external forcing, and they proved global existence of weak solutions for the Cauchy problem with nonlinear diffusion for the cell density.About:
This article is published in Annales de l'Institut Henri Poincaré C, Analyse non linéaire.The article was published on 2011-09-01 and is currently open access. It has received 247 citations till now. The article focuses on the topics: Space (mathematics) & Initial value problem.read more
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Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues
TL;DR: In this article, a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller-Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions.
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Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops
TL;DR: In this paper, coupled chemotaxis (Navier and Stokes) systems generalizing the prototype have been proposed to describe the collective effects arising in bacterial suspensions in fluid drops, and they have been applied to the model of collective effects of bacterial suspensions.
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Stabilization in a two-dimensional chemotaxis-Navier–Stokes system
TL;DR: In this paper, an initial-boundary value problem for the system of swimming aerobic bacteria has been studied and a global-in-time classical solution has been shown to stabilize to the spatially uniform equilibrium.
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Global weak solutions in a three-dimensional chemotaxis–Navier–Stokes system
TL;DR: In this paper, the chemotaxis-Navier-stokes system (0.1) is considered under homogeneous boundary conditions of Neumann type for n and Dirichlet type for u, in a bounded convex domain Ω ⊂ R 3 with smooth boundary.
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Eventual smoothness and stabilization of large-data solutions in a three-dimensional chemotaxis system with consumption of chemoattractant
Youshan Tao,Michael Winkler +1 more
TL;DR: In this paper, it was shown that for arbitrarily large initial data, this problem admits at least one global weak solution for which there exists T > 0 such that ( u, v ) is bounded and smooth in Ω × (T, ∞ ).
References
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Book
Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models
TL;DR: In this article, the Navier-Stokes equations and the Euler equations are studied in the context of nonlinear partial differential equations (NPDE) and their applications in applied mathematics.
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Bacterial Swimming and Oxygen Transport Near Contact Lines
Idan Tuval,Luis Cisneros,Christopher Dombrowski,Charles W. Wolgemuth,John O. Kessler,Raymond E. Goldstein +5 more
TL;DR: Using the geometry of a sessile drop, in suspensions of Bacillus subtilis the self-organized generation of a persistent hydrodynamic vortex is demonstrated that traps cells near the contact line and enhances uptake of oxygen into the suspension.
Journal Article
Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions
TL;DR: The Keller-Segel system describes the collective motion of cells which are attracted by a chemical substance and are able to emit it in its simplest form it is a conservative drift-diffusion equation coupled to an elliptic equation for the chemo-attractant concentration as mentioned in this paper.
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Global Solutions to the Coupled Chemotaxis-Fluid Equations
TL;DR: In this paper, a model arising from biology, which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and externa...