Well-posedness on a new hydrodynamic model of the fluid with the dilute charged particles

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Wang, Yong^1,2,3  Liu, Chun³  Tan, Zhong^1,2 

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

[2] Xiamen Univ, Fujian Prov Key Lab Math Modeling & Sci Comp, Xiamen 361005, Fujian, Peoples R China

[3] Penn State Univ, Dept Math, University Pk, PA 16802 USA

关键词: Poisson-Nemst-Planck-Navier-Stokes equations;    Energetic variational approach;    Well-posedness;    Optimal decay;   

DOI  :  10.1016/j.jde.2016.09.026

来源: Elsevier

【 摘 要 】

We use an energetic variational approach to derive a new hydrodyrirmic model, which could be called a generalized Poisson-Nemst-Planck-Navier-Stokes system. Such the system could describe the dynamics of the compressible conductive fluid with the dilute charged particles and be used to analyze the interactions between the macroscopic fluid motion and the microscopic charge transportation. Then, we develop a general method to obtain the unique local classical solution, the unique global solution under small perturbations and the optimal decay rates of the solution and its derivatives of any order. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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