Global Zero-relaxation Limit Problem of the Electro-diffusion Model Arising in Electro-Hydrodynamics
作者机构：Department of MathematicsJiangxi University of Finance and EconomicsNanchang330032China School of Public AdministrationGuangdong University of Foreign StudiesGuangzhou510006China College of Mathematics and StatisticsNorthwest Normal UniversityLanzhou730070China
出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)
年 卷 期：2024年第40卷第1期
页 面：241-268页
核心收录：
学科分类：07[理学] 080103[工学-流体力学] 08[工学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 070101[理学-基础数学]
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)
主 题：fourier-Herz space littlewood-Paley decomposition stability limit dissipative system
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 *** 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.
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