Relaxation-time limit of the multidimensional bipolar hydrodynamic model in Besov space

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Li, Yeping²  Zhang, Ting¹ 

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China

[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

关键词: Relaxation-time limit;    Bipolar;    Hydrodynamic model;    Besov space;    Drift-diffusion model;   

DOI  :  10.1016/j.jde.2011.07.018

来源: Elsevier

【 摘 要 】

In this paper, we study a multidimensional bipolar hydrodynamic model for semiconductors or plasmas. This system takes the form of the bipolar Euler-Poisson model with electric field and frictional damping added to the momentum equations. In the framework of the Besov Space theory, we establish the global existence of smooth solutions for Cauchy problems when the initial data are sufficiently close to the constant equilibrium. Next, based on the special structure of the nonlinear system, we also show the uniform estimate of solutions with respect to the relaxation time by the high- and low-frequency decomposition methods. Finally we discuss the relaxation-time limit by compact arguments. That is, it is shown that the scaled classical solution strongly converges towards that of the corresponding bipolar drift-diffusion model, as the relaxation time tends to zero. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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