| Abstrakt: |
In this paper, we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes equations. That is, the paper deals with a singular limit problem of { u t ε + u ε ⋅ ∇ u ε − Δ u ε + ∇ P ε = Δ ϕ ε ∇ ϕ ε , i n R 3 × (0 , ∞) ∇ ⋅ u ε = 0 , i n R 3 × (0 , ∞) n t ε + u ε ⋅ ∇ n ε − Δ n ε = − ∇ ⋅ (n ε ∇ ϕ ε) , i n R 3 × (0 , ∞) c t ε + u ε ⋅ ∇ c ε − Δ c ε = ∇ ⋅ (c ε ∇ ϕ ε) , i n R 3 × (0 , ∞) ε − 1 ϕ t ε = Δ ϕ ε − n ε + c ε , i n R 3 × (0 , ∞) (u ε , n ε , c ε , ϕ ε) | t = 0 = (u 0 , n 0 , c 0 , ϕ 0) , i n R 3 involving with a positive, large parameter ϵ. The present work show a case that (uϵ, nϵ, cϵ) stabilizes to (u∞, n∞, c∞):= (u, n, c) uniformly with respect to the time variable as ϵ → + ∞ with respect to the strong topology in a certain Fourier-Herz space. [ABSTRACT FROM AUTHOR] |
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