2011 # Blow-up solutions to Landau-Lifshitz-Maxwell systems

**Abstract:** Communicated by B. StraughanThe Landau-Lifshitz-Gilbert equation describes the evolution of spin fields in continuum ferromagnetics. The present paper consists of two parts. The first one is to prove the local existence of smooth solution to the Landau-LifshitzMaxwell systems in dimensions three. The second is to prove the finite time blow up of solutions for these systems. It states that for suitably chosen initial data, the short time smooth solutions to the Landau-Lifshitz-Maxwell equations do blow up at fi…

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2018

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“…However, Ding et al [29] proved that = 3 or = 4 dimensional LLE with the Gilbert term will lead to a finite time blowup under specific initial boundary conditions. Some regularity and blowup results for LLE were derived considering the Maxwell field [30,31].…”

confidence: 99%

“…However, Ding et al [29] proved that = 3 or = 4 dimensional LLE with the Gilbert term will lead to a finite time blowup under specific initial boundary conditions. Some regularity and blowup results for LLE were derived considering the Maxwell field [30,31].…”

confidence: 99%