可压磁流体方程组弱解能量的有界性

Bounded Energy of Weak Solutions of Compressible Magnetohydrodynamic Equations

研究可压缩磁流体(MHD)方程组的弱解在三维有界区域上关于时间的全局行为.为了解决MHD方程组的这一问题,需要对磁场项、耦合项以及流体项进行估计.对非线性项(▽×M)×M的处理方式是受可压Navier-Stokes方程组的启发.利用Yong不等式、Hlder不等式以及Soblev不等式等对弱解进行能量估计.对绝热指数进行适当限制,证明了在有界外力作用下,总能量是有界的.

We consider the global behavior of weak solutions of the equations of compressible magnetohydrodynamic（MHD） flows in time in a bounded three-dimesion domain-arbitrary forces. To achieve our goal for the MHD problem, we also need to develop esti- mates to deal with the magnetic field and its coupling and interacting with the fluid variables. The nonlinear term （△↓ × M） ）× M will be dealt with by the idea arising in compressible Navier-Stokes equations. We use Yong inequality, Holder inequality and Soblev ine-quality for energy estimate. Under certain restrictions imposed on the adiabatic constant,we proved that total energy of finite energy weak solution is still bounded when the external force is bounded.