ASYMPTOTIC BEHAVIORS FOR THE FULL COMPRESSIBLE QUANTUM NAVIER-STOKES-MAXWELL EQUATIONS WITH GENERAL INITIAL DATA

摘要

In this paper, we study the asymptotic behaviors for the quantum Navier-Stokes-Maxwell equations with general initial data in a torus T-3. 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.