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Asymptotic dynamics on a chemotaxis-Navier–Stokes system with nonlinear diffusion and inhomogeneous boundary conditions
https://doi.org/10.1142/S0218202520500244Cited by:23 (Source: Crossref)
Abstract
The diffusion of cells in a viscous incompressible fluid (e.g. water) may be viewed like movement in a porous medium and there is a bidirectorial oxygen exchange between water and their surrounding air in thin fluid layers near the air–water contact surface. This leads to the following chemotaxis-Navier–Stokes system with nonlinear diffusion:
{nt+u⋅∇n=Δnm−∇⋅(n∇c),x∈Ω, t>0,ct+u⋅∇c=Δc−nc,x∈Ω, t>0,ut+(u⋅∇)u=Δu+∇P+n∇ϕ,x∈Ω, t>0,∇⋅u=0,x∈Ω, t>0,
∂nm∂ν=n∂c∂ν,∂c∂ν+a1(x)c=a2(x,t),u=0,x∈∂Ω,t>0,
n(⋅,t)→¯n0,c(⋅,t)→0,andu(⋅,t)→0
Communicated by M. Winkler
Keywords:
AMSC: 35K55, 35Q92, 35Q35, 92C17
