Large time behavior for the non‐isentropic Navier–Stokes–Maxwell system |
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| Authors: | Qingqing Liu Yifan Su |
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| Affiliation: | 1. (QQL) School of Mathematics, South China University of Technology, Guangzhou, China;2. (YFS) The Hubei Key Laboratory of Mathematical Physics, School of Mathematics and Statistics, Central China Normal University, Wuhan, China |
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| Abstract: | In this paper, we are concerned with the system of the non‐isentropic compressible Navier–Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The global existence of solutions near constant steady states is established, and the time‐decay rates of perturbed solutions are obtained. The proof for existence is due to the classical energy method, and the investigation of large‐time behavior is based on the linearized analysis of the non‐isentropic Navier–Stokes–Poisson equations and the electromagnetic part for the linearized isentropic Navier–Stokes–Maxwell equations. In the meantime, the time‐decay rates obtained by Zhang, Li, and Zhu [J. Differential Equations, 250(2011), 866‐891] for the linearized non‐isentropic Navier–Stokes–Poisson equations are improved. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | asymptotic behavior of solutions Navier– Stokes equations Maxwell equations subclass 35B40 35Q30 35Q61 |
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