磁流体方程的时间解析性和时间周期解

Time analyticity and periodic solutions for magnetohydrodynamics equations

考查了周期边界条件下的磁流体方程,证明了它的解关于时间是解析的,由此得到了磁流体方程的解的向后惟一性.对于周期解,证明了当周期小于某个常数时,周期的弱解是强解,进一步地这样的强解是定常解.

Magnetohydrodynamics equations with periodic boundary conditions are considered in this note. The time analyticity of the solutions for the equations is proved and the backward uniqueness is obtained. As for the periodic weak solutions it is proved that the weak periodic solutions are actually strong solutions when the period is smaller than a certain constant ,and furthermore such strong solutions are necessarily stationary when the periods are small enough.