ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS

doi:10.1016/S0252-9602(15)30030-8

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 955-969.doi: 10.1016/S0252-9602(15)30030-8

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ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS

冯跃红^1,2, 王术³, 李新⁴

1. College of Applied Sciences, Beijing University of Technology, Beijing 100022, China;
2. Laboratoire de Mathématiques, Université Blaise Pascal, Clermont-Ferrand, 63000, France;
3. College of Applied Sciences, Beijing University of Technology, Beijing 100022, China;
3. Department of Mathematics and Computer Science, Xinyang Vocational and Technical College, Xinyang 464000, China

收稿日期:2014-10-30 修回日期:2015-02-14 出版日期:2015-09-01 发布日期:2015-09-01
作者简介:Shu WANG, E-mail: wangshu@bjut.edu.cn; Shu WANG, E-mail: wangshu@bjut.edu.cn; Xin LI, E-mail: lixin91600@163.com
基金资助:
The authors are supported by the Collaborative Innovation Center on Beijing Society-building and Social Governance, NSFC (11371042), BNSF (1132006), the key fund of the Beijing education committee of China and China Postdoctoral Science Foundation funded project.

ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS

Yuehong Feng^1,2, Shu Wang³, Xin Li⁴

1. College of Applied Sciences, Beijing University of Technology, Beijing 100022, China;
2. Laboratoire de Mathématiques, Université Blaise Pascal, Clermont-Ferrand, 63000, France;
3. College of Applied Sciences, Beijing University of Technology, Beijing 100022, China;
3. Department of Mathematics and Computer Science, Xinyang Vocational and Technical College, Xinyang 464000, China

Received:2014-10-30 Revised:2015-02-14 Online:2015-09-01 Published:2015-09-01
Supported by:
The authors are supported by the Collaborative Innovation Center on Beijing Society-building and Social Governance, NSFC (11371042), BNSF (1132006), the key fund of the Beijing education committee of China and China Postdoctoral Science Foundation funded project.

摘要/Abstract

摘要：

This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in R³. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm||·||_H^s-1, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than||·||_H^s-1. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.

关键词: bipolar compressible Navier-Stokes-Maxwell system, plasmas, global smooth solutions, energy estimates, large-time behavior

Abstract:

Key words: bipolar compressible Navier-Stokes-Maxwell system, plasmas, global smooth solutions, energy estimates, large-time behavior

中图分类号:

35L45

冯跃红, 王术, 李新. ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS[J]. 数学物理学报(英文版), 2015, 35(5): 955-969.

Yuehong Feng, Shu Wang, Xin Li. ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS[J]. Acta mathematica scientia,Series B, 2015, 35(5): 955-969.

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ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS

ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS

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