Abstract
In this paper, we study the asymptotic behaviors for the quantum Navier-Stokes-Maxwell equations with general initial data in a torus \begin{document}$\mathbb{T}^{3}$\end{document} . Based on the local existence theory, we prove the convergence of strong solutions for the full compressible quantum Navier-Stokes-Maxwell equations towards those for the incompressible e-MHD equations plus the fast singular oscillating in time of the sequence of solutions as the Debye length goes to zero. We also mention that similar arguments can be applied to the Euler-Maxwell system. Remarkably, we eliminate the highly oscillating terms produced by the general initial data by using the formal two-timing method. Moreover, using the curl-div decomposition and elaborate energy estimates, we derive uniform (in the Debye length) estimates for the remainder system.
Highlights
The purpose of this paper is to consider the following full quantum Navier-Stokes-Maxwell system with general initial data, which describes the transport of viscous charged particles for a plasma [1, 3, 10, 11, 13, 15]
The main result of this paper is stated in Theorem 2.4
If these coefficients μ, ν, κ, are zero, we prove Theorem 2.5 by using the similar method to that used in the proof of Theorem 2.4
Summary
The purpose of this paper is to consider the following full quantum Navier-Stokes-Maxwell system with general initial data, which describes the transport of viscous charged particles for a plasma [1, 3, 10, 11, 13, 15]. In order to overcome the strong oscillation and obtain the asymptotic expansion by the slow and fast time in the divergence-free vector fields, we further divide the operator P defined in (15) into Putting the above expansion (36) into system (5) and combining the incompressible system (7) together with the fast oscillation systems (33) and (34), we have the following linear system satisfied by the fast second order oscillation term,
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