Some recent results on the well-posedness of solutions and the regularity of weak solutions to the Landau-Lifshitz equation

• 1、College of Mathematics and Statistics, Chongqing University, Chongqing 401331

Abstract：\justifying{The micro-magnetic theory developed based on the Landau-Lifshitz equation can accurately describe the microscopic physical processes of magnetodynamics. Its related mathematical theories have been widely applied in the development of high-performance magnetic recording devices, which has attracted widespread attention from many mathematicians and physicists. In recent decades, numerous scholars have studied the mathematical theories of the Landau-Lifshitz equation and other related equations. In this paper, we mainly introduce the research progress on the well-posedness of solutions to the Landau-Lifshitz equation and the Landau-Lifshitz-Gilbert equation, as well as the regularity problem of weak solutions to the Landau-Lifshitz equation. }

Keywords： \justifying{applied mathematics the Landau-Lifshitz equation well-posedness the regularity of weak solution monotonicity inequality}