Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7221807 | Nonlinear Analysis: Real World Applications | 2019 | 27 Pages |
Abstract
This paper investigates an incompressible chemotaxis-Navier-Stokes system with slow p-Laplacian diffusion nt+uâ
ân=ââ
(|ân|pâ2ân)âââ
(nÏ(c)âc),xâΩ,t>0,ct+uâ
âc=Îcânf(c),xâΩ,t>0,ut+(uâ
â)u=Îu+âP+nâΦ,xâΩ,t>0,ââ
u=0,xâΩ,t>0under homogeneous boundary conditions of Neumann type for n and c, and of Dirichlet type for u in a bounded convex domain ΩâR3 with smooth boundary. Here, ΦâW1,â(Ω), 0<ÏâC2([0,â)) and 0â¤fâC1([0,â)) with f(0)=0. It is proved that if p>3215
and under appropriate structural assumptions on f and Ï, for all sufficiently smooth initial data (n0,c0,u0) the model possesses at least one global weak solution.
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Authors
Weirun Tao, Yuxiang Li,