Blow-up solutions to Landau-Lifshitz-Maxwell systems

The 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–Lifshitz–Maxwell 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 finite time. Copyright © 2011 John Wiley & Sons, Ltd.