直角坐标系下三维轴对称非齐次不可压缩MHD方程的基本能量估计

考虑到三维轴对称非齐次不可压缩MHD方程的基本能量估计对后续解的存在性的证明至关重要,为了使其适用范围更广,在柱坐标下的MHD方程基本能量估计的基础上,通过移除其柱对称条件,在直角坐标系的情况下,给出了MHD方程基本能量估计中每一个子项的详细推导过程,充分利用MHD方程在直角坐标系下的质量守恒公式和不可压缩条件,最终推导得到MHD方程在直角坐标系下的基本能量估计.

Elementary energy estimates of three-dimensional axially symmetric nonhomogeneous incompressible MHD equations under the rectangular coordinate system

It is known that elementary energy estimates of three-dimensional axially symmetric nonhomogeneous incompressible MHD equations is crucial for the global existence of the subsequent solution to MHD equations. In order to make it applied widely, by relying on elementary energy estimates of three-dimensional axially symmetric MHD equations under the cylindrical coordinate system and removing the constraint condition of the cylindrical coordinate, the problem-solving process of each of the items in elementary energy estimates of MHD equations is explicitly given under the rectangular coordinate system. Finally, by making full use of mass conservation formula and the incompressible constraint condition of MHD equations under the rectangular coordinate system, elementary energy estimates of MHD equations under the rectangular coordinate system are successfully deduced.