Global weak solutions for the three-dimensional chemotaxis-Navier-Stokes system with nonlinear diffusion

We consider an initial-boundary value problem for the incompressible chemotaxis-Navier-Stokes equations generalizing the porous-medium-type diffusion model \( \quad n_t+u\cdot\nabla n=\Delta n^m-\nabla\cdot(n\chi(c)\nabla c), \) \( \quad c_t+u\cdot\nabla c=\Delta c-nf(c), \) \( \quad u_t+\kappa(u\cd...

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Bibliographic Details
Published in:arXiv.org 2015-01
Main Authors: Zhang, Qingshan, Li, Yuxiang
Format: Article
Language:English
Subjects:
Boundary value problems
Computational fluid dynamics
Fluid flow
Navier-Stokes equations
Porous media
Online Access:Get full text
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Summary:We consider an initial-boundary value problem for the incompressible chemotaxis-Navier-Stokes equations generalizing the porous-medium-type diffusion model \( \quad n_t+u\cdot\nabla n=\Delta n^m-\nabla\cdot(n\chi(c)\nabla c), \) \( \quad c_t+u\cdot\nabla c=\Delta c-nf(c), \) \( \quad u_t+\kappa(u\cdot\nabla)u=\Delta u+\nabla P+n\nabla\Phi, \) \( \quad \nabla\cdot u=0, \) in a bounded convex domain \(\Omega\subset\mathbb{R}^3\). It is proved that if \(m\geq\frac{2}{3}\), \(\kappa\in\mathbb{R}\), \(0
ISSN:2331-8422