MILD ILL-POSEDNESS FOR 2D MAGNETO-MICROPOLAR FLUID EQUATIONS NEAR A BACKGROUND MAGNETIC FIELD.

The global well-posedness for the 2D inviscid magneto-micropolar fluid (MMPF) equations remains an open problem. It is well known that the global boundedness of the L∞ -norm of the vorticity ω yields the resolution. This paper studies the growth of || ω || L∞ from a different perspective and shows that there exists a sequence of small initial vorticity approaching zero in the L∞ -norm such that the corresponding || ω || L∞ can grow to be uniformly bounded from below in a short time for MMPF equations near a special steady state. Specifically, the vorticity is mildly ill-posed in the L∞ -norm. [ABSTRACT FROM AUTHOR]