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

• Published in: Acta mathematica scientia Vol. 35; no. 5; pp. 955 - 969
• Main Author: 冯跃红 王术 李新
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2015; College of Applied Sciences, Beijing University of Technology, Beijing 100022, China; Laboratoire de Mathématiques, Université Blaise Pascal, Clermont-Ferrand, 63000, France%College of Applied Sciences, Beijing University of Technology, Beijing 100022, China%Department of Mathematics and Computer Science, Xinyang Vocational and Technical College,Xinyang 464000, China
• Subjects: 35L45; 35L60; 35Q60; bipolar compressible Navier-Stokes-Maxwell system; energy estimates; global smooth solutions; large-time behavior; l系统; Navier-Stokes; plasmas; 双极性; 可压缩; 平衡态; 整体光滑解; 渐近行为; 等离子体; energy estimates; plasmas; 35L60; 35L45; global smooth solutions; 35Q60; bipolar compressible Navier-Stokes-Maxwell system; large-time behavior
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(15)30030-8

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 R^3. 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.