共面磁场中两平行平板间层流稳定性吸引域半径的研究

考虑一水平方向无限的夹层，夹层中充满均匀的不可压缩的黏性导电流体，其中与流体相邻的介质是不导电的，并且夹层处于共面磁场中。文献4]和5]通过定义不同的广义能量泛函对该问题的层流解的非线性稳定性进行研究，并分别得到了层流解条件稳定的充分条件，本文通过比较这两篇文献中不同广义能量泛函下稳定性吸引域半径的大小来比较不同广义能量泛函的优劣。吸引域半径对比结果表明，共面磁场会导致文献4]中的吸引域半径减小，但不会影响文献5]中的吸引域半径。

The radius of the stability ball of laminar flow between parallel planes in the presence of a coplanar magnetic field

We consider an incompressible fluid layer with infinite horizontal uniform viscous conductivity, in which the medium adjacent to the fluid is non-conductive and the interlayer is in a coplanar magnetic field. Two previous papers in the literature have studied the nonlinear stability of the laminar solution of this problem by defining different generalized energy functionals, and obtained sufficient conditions for the stability of the laminar solution. In this paper, the advantages and disadvantages of different generalized energy functions are compared by comparing the radius of the stability ball for the two generalized energy functions employed in the previous two papers. It is found that the coplanar magnetic field will reduce the radius of the stability ball in one case, but will not affect the radius of the stability ball in the other case.