摘要
We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1＋n to the unit sphere S2, 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.
We consider the Cauchy problem for evolutionary Faddeev model corresponding to maps from the Minkowski space R^1＋n to the unit sphere S2, 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.
基金
The first author is partly supported by National Natural Science Foundation of China （Grants Nos. 10801029 and 10911120384）, FANEDD, Shanghai Rising Star Program （10QA1400300）, SGST 09DZ2272900 and SRF for ROCS, SEM
the second author is partly supported by an NSF grant
the third author is partly supported by the National Natural Science Foundation of China （Crant No. 10728101）, the 973 project of the Ministry of Science and Technology of China, the Doctoral Program Foundation of the Ministry of Education of China, the ＂111＂ project （B08018） and SGST 09DZ2272900Acknowledgements Part of the work was carried out when Zhen Lei was visiting the Courant Institute. He would like to thank Professor Fanghua Lin for his hospitality.
