Mild ill-posedness in L∞ for 2D magnetohydrodynamic system with damping

作者：Fang, Hui; Bie, Qunyi^*

来源：Journal of Differential Equations, 2023, 377: 519-543.

DOI：10.1016/j.jde.2023.09.013

• Magnetohydrodynamic equation
• Stability
• Ill-posedness

The present paper is devoted to the initial-value problem for the incompressible magnetohydrodynamic system in two-dimensional space where the velocity equation involves no dissipation and the vertical component equation has a damping. Here we concentrate on the stability problem for the magnetohydrodynamic system. By constructing a sequence of special initial data, we show that the solution map of vorticity is discontinuous. Our result indicates that the L infinity-norm of the vorticity is mildly ill-posed.

• 单位
  哈尔滨工程大学