在这份报纸，我们为下列伪线性的波浪方程 utt-2kuxxt=(unx ) 学习 Cauchy 问题 x k0 并且是 2 是的实数，和 n 一个整数。我们证明为任何 T0， Cauchy 问题承认唯一的全球光滑的答案 u C ((0， T ] ；H (R)) C ([0， T ] ；H2 (R)) C1 ...在这份报纸，我们为下列伪线性的波浪方程 utt-2kuxxt=(unx ) 学习 Cauchy 问题 x k0 并且是 2 是的实数，和 n 一个整数。我们证明为任何 T0， Cauchy 问题承认唯一的全球光滑的答案 u C ((0， T ] ；H (R)) C ([0， T ] ；H2 (R)) C1 ([0， T ] ；L2 (R)) 在起始的数据上的合适的假设下面。展开更多
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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China(10371073)
文摘在这份报纸，我们为下列伪线性的波浪方程 utt-2kuxxt=(unx ) 学习 Cauchy 问题 x k0 并且是 2 是的实数，和 n 一个整数。我们证明为任何 T0， Cauchy 问题承认唯一的全球光滑的答案 u C ((0， T ] ；H (R)) C ([0， T ] ；H2 (R)) C1 ([0， T ] ；L2 (R)) 在起始的数据上的合适的假设下面。
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.
文摘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.
