Global Solutions of Evolutionary Faddeev Model With Small Initial Data

Details Global Solutions of Evolutionary Faddeev Model With Small Initial Data Global Solutions of Evolutionary Faddeev Model With Small Initial Data

2012-03-13

arxiv.org/abs/1203.2696v1

Acta Mathematica Sinica, 27 (2011), no. 2, 309-328 Acta Mathematica Sinica Acta Mathematica Sinica Acta Mathematica Sinica, Vo

Mathematics

Analysis of PDEs

Scientific paper

We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space $\mathbb{R}^{1 + n}$ to the unit sphere $\mathbb{S}^2$, which obey a system of non-linear wave equations. The nonlinearity enjoys the null structure and contains semi-linear terms, quasi-linear terms and unknowns themselves. We prove that the Cauchy problem is globally well-posed for sufficiently small initial data in Sobolev space.

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