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Stability of non-constant equilibrium solutions for two-fluid Euler–Maxwell systems
Institution:1. College of Applied Sciences, Beijing University of Technology, Beijing 100022, China;2. Clermont Université, Université Blaise Pascal, 63000 Clermont-Ferrand, France;3. Laboratoire de Mathématiques, CNRS-UMR 6620, Complexe scientifique Les Cézeaux, BP 80026, 63171 Aubière cedex, France;1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, PR China;2. School of Mathematics, Georgia Tech, Atlanta 30332, USA;1. Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070, PR China;2. The Institute of Mathematical Sciences, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong;3. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, PR China;1. School of Mathematics, Liaoning University, Shenyang 110036, PR China;2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China;1. Department of Mathematics, Donghua University, China;2. School of Mathematical Sciences, Shanghai Jiao Tong University, China;1. College of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;2. School of Mathematics, East China University of Science and Technology, Shanghai 200237, China
Abstract:In this work we consider periodic problems for two-fluid compressible Euler–Maxwell systems for plasmas. The initial data are supposed to be in a neighborhood of non-constant equilibrium states. Mainly by an induction argument used in Peng (2015), we prove the global stability in the sense that smooth solutions exist globally in time and converge to the equilibrium states as the time goes to infinity. Moreover, we obtain the global stability of solutions with exponential decay in time near the equilibrium states for two-fluid compressible Euler–Poisson systems.
Keywords:Two-fluid Euler–Maxwell system  Plasmas  Non-constant equilibrium solutions  Global smooth solutions  Long time behavior
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