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

摘要

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.

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