Weighted The Landau-lifshitz Systems-gilbert Equations Blasting

Using the slice energy monotonicity formula for weighted Landau-Lifshitz-Gilbert equa-tion in low dimensions, the local Hardy space estimate, the duality between Hardy andBMO spaces, we obtain that in dimensions three or four, for suitably chosen initial data,the short time smooth solution to the weighted Landau-Lifshitz-Gilbert equation blows upat finite time.