Global solutions of the evolutionary Faddeev model with small initial data |
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| Authors: | Zhen Lei Fang Hua Lin Yi Zhou |
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| Institution: | [1]School of Mathematical Sciences ; LMNS and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai 200433, P. R. China [2]Courant Institute of Mathematics, New York University, NY 10012, USA |
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| Abstract: | We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space ℝ1+n
to the unit sphere $
\mathbb{S}
$
\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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| Keywords: | Faddeev model global existence quasi-linear wave equations semi-linear wave equations |
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