论文标题
在3D有限域中具有较大振荡和真空的3D有界域中的全球全球良好性
Global Well-Posedness of Full Compressible Magnetohydrodynamic System in 3D Bounded Domains with Large Oscillations and Vacuum
论文作者
论文摘要
研究了三维（3D）完整可压缩的磁性水力动力系统，以通用界面域中的速度条件为速度，用于温度的绝热条件和磁场的完美传导。对于具有较小能量但可能较大的振荡的常规初始数据，可以获得经典和弱解的全球存在以及该系统初始值问题的指数衰减速率。特别是，这种经典溶液的密度和温度最初都可以消失。此外，还表明，对于经典溶液，当初始真空出现时（即使在一个点）时，密度的振荡将以指数速率毫无根据。开发了一些新的观察结果和有用的估计，以克服滑动边界条件引起的困难。
The three-dimensional (3D) full compressible magnetohydrodynamic system is studied in a general bounded domain with slip boundary condition for the velocity filed, adiabatic condition for the temperature and perfect conduction for the magnetic field. For the regular initial data with small energy but possibly large oscillations, the global existence of classical and weak solution as well as the exponential decay rate to the initial-boundary-value problem of this system is obtained. In particular, the density and temperature of such a classical solution are both allowed to vanish initially. Moreover, it is also shown that for the classical solutions, the oscillation of the density will grow unboundedly with an exponential rate when the initial vacuum appears (even at a point). Some new observations and useful estimates are developed to overcome the difficulties caused by the slip boundary conditions.
