Sharp well-posedness and ill-posedness the Chern-Simons-Dirac system in one dimension
Sharp well-posedness and ill-posedness the Chern-Simons-Dirac system in one dimension
复制标题
一维陈-西蒙斯-狄拉克系统的尖锐适定性和不适定性
DOI：
10.1093/imrn/rnv160
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Shuji Machihara and Mamoru Okamoto
中科院分区：
文献类型：
--
作者：
Junichiro Katsuta;Yasunobu Uchiyama;Stefan Funk;Shuji Machihara and Mamoru Okamoto
我们完成了一维Chern-Simons-Dirac系统Cauchy问题的适定性或不适定性的Sobolev正则性范围的分离。我们给出了答案，其余的情况下，从以前的作品Bournaveas等人。和Machihara和冈本。其余的情况下，从缩放的角度来看，对应于临界或准超临界的情况。我们还将以前在无质量条件下的不适定结果推广到相应的有质量条件下。
We reach completion of separation for the range of Sobolev regularity for well-posedness or ill-posedness of the Cauchy problem for the Chern–Simons–Dirac system in one spatial dimension. We give the answers for the remaining cases from the previous works by Bournaveas et al. and Machihara and Okamoto . The remaining cases correspond to the critical or quasi-super-critical cases from the point of view of scaling. We also extend the previous ill-posed results under the massless setting to the corresponding massive setting.