摘要
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)+u^(∈)·▽u^(∈)-Δu^(∈)+▽P^(∈)=Δφ^(∈)▽φ^(∈),in R^(3)×(0,∞),▽·u^(∈)=0,in R^(3)×(0,∞),n^(∈)_(t)+u^(∈)·▽n^(∈)-Δn^(∈)=-▽·(n^(∈)▽φ^(∈)),in R^(3)×(0,∞),ct+u^(∈)·▽c^(∈)-Δc^(∈)=▽·(c^(∈)▽φ^(∈)),in R^(3)×(0,∞),∈^(-1)φ^(∈)_(t)=Δφ^(∈)-n^(∈)+c^(∈),in R^(3)×(0,∞),(u^(∈),n^(∈),c^(∈),φ^(∈))|t=0=(u0,n0,c0,φ0),in R^(3) involving with a positive,large parameter^(∈).The present work show a case that(u^(∈),n^(∈),c^(∈))stabilizes to(u^(∞),n∞,c∞):=(u,n,c)uniformly with respect to the time variable as^(∈)→+∞with respect to the strong topology in a certain Fourier-Herz space.
基金
partial supported by the National Natural Science Foundation of China (Grant Nos. 12161041, 11801236)
Training Program for academic and technical leaders of major disciplines in Jiangxi Province (Grant No.20204BCJL23057)
Natural Science Foundation of Jiangxi Province (Grant Nos.20212BAB201008 and 20232BAB201013)
partial supported by the National Natural Science Foundation of China (Grant Nos. 12001435, 12361050)
College Teachers Innovation Fund Project of Gansu Provincial Education Department (2023A-002)。
