# American Institute of Mathematical Sciences

December  2013, 2(4): 599-620. doi: 10.3934/eect.2013.2.599

## On Landau-Lifshitz equations of no-exchange energy models in ferromagnetics

 1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States 2 Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824, United States

Received  September 2012 Revised  February 2013 Published  November 2013

In this paper, we study Landau-Lifshitz equations of ferromagnetism with a total energy that does not include a so-called exchange energy. Many problems, including existence, stability, regularity and asymptotic behaviors, have been extensively studied for such equations of models with the exchange energy. The problems turn out quite different and challenging for Landau-Lifshitz equations of no-exchange energy models because the usual methods based on certain compactness do not apply. We present a new method for the existence of global weak solution to the Landau-Lifshitz equation of no-exchange energy models based on the existence of regular solutions for smooth data and certain stability of the solutions. We also study higher time regularity, energy identity and asymptotic behaviors in some special cases for weak solutions.
Citation: Wei Deng, Baisheng Yan. On Landau-Lifshitz equations of no-exchange energy models in ferromagnetics. Evolution Equations & Control Theory, 2013, 2 (4) : 599-620. doi: 10.3934/eect.2013.2.599
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