Mild Ill-Posedness in<i>L</i>โ for 2D Resistive MHD Equations Near a Background Magnetic Field
Mild Ill-Posedness in<i>L</i>โ for 2D Resistive MHD Equations Near a Background Magnetic Field
Abstract The global well-posedness on the 2D resistive MHD equations without kinematic dissipation remains an outstanding open problem. This is a critical problem. Any $L^p$-norm of the vorticity $\omega $ with $1\le p&lt;\infty $ has been shown to be bounded globally (in time), but whether the $L^\infty $-norm of $\omega โฆ