In this article we consider a Cauchy problem for the full compressible Navier–Stokes–Maxwell system arising from viscosity plasmas. This system is quasilinear hyperbolic–parabolic. With the help of techniques of symmetrizers and the smallness of non-constant equilibrium solutions, we establish that global smooth solutions exist and converge to the equilibrium solution as the time approaches infinity. This result is obtained for initial data close to the steady-states. As a byproduct, we obtain the global stability of solutions near the equilibrium states for the full compressible Navier–Stokes–Poisson system in a three-dimensional torus.

中文翻译：

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完全可压缩Navier–Stokes–Maxwell系统的非常数平衡解的稳定性

在本文中，我们考虑了由粘性等离子体引起的完整可压缩Navier–Stokes–Maxwell系统的柯西问题。该系统是拟线性双曲-抛物线。借助于对称化技术和非恒定平衡解的较小性，我们建立了整体光滑解的存在，并随着时间趋于无穷大而收敛到平衡解。对于接近稳态的初始数据可获得此结果。作为副产品，我们获得了三维圆环中完全可压缩的Navier–Stokes–Poisson系统在平衡态附近的溶液的全局稳定性。