On The 1+2 Dimensional Landau-Lifshitz Equation

Qing Ding

On The 1+2 Dimensional Landau-Lifshitz Equation

Differential Geometry 2007-05-23 v1 Mathematical Physics math.MP

Authors: Qing Ding

Abstract

By using the geometric concept of PDEs with prescribed curvature representations, we show that the 1+2 dimensional Landau-Lifshitz equation is gauge equivalent to a 1+2 dimensional nonlinear Schr\"odinger-type system. From the nonlinear Schr\"odinger-type system, we construct blowing up $H^3({\bf R}^2)$ -solutions to the 1+2 dimensional Landau-Lifshitz equation, which reveals the blow up phenomenon of the equation.

Keywords

blow-up for partial differential equations blow-up

Cite

@article{arxiv.math/0504288,
  title  = {On The 1+2 Dimensional Landau-Lifshitz Equation},
  author = {Qing Ding},
  journal= {arXiv preprint arXiv:math/0504288},
  year   = {2007}
}

Comments

26 pages without figures

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