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Large time behavior for the non‐isentropic Navier–Stokes–Maxwell system
Author(s) -
Liu Qingqing,
Su Yifan
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3999
Subject(s) - isentropic process , mathematics , navier–stokes equations , maxwell's equations , compressibility , constant (computer programming) , non dimensionalization and scaling of the navier–stokes equations , mathematical analysis , lorentz transformation , classical mechanics , physics , mechanics , computer science , programming language
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.