Well-posedness in Gevrey function space for the three-dimensional Prandtl equations

Wei-Xi Li Tong Yang

Analysis of PDEs mathscidoc:1912.431009

arXiv preprint arXiv:1708.08217, 2017.8
In the paper, we study the three-dimensional Prandtl equations, and prove that if one component of the tangential velocity field satisfies the monotonicity assumption in the normal direction, then the system is locally well-posed in the Gevrey function space with Gevrey index in ] 1, 2]. The proof relies on some new cancellation mechanism in the system in addition to those observed in the two-dimensional setting.
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@inproceedings{wei-xi2017well-posedness,
  title={Well-posedness in Gevrey function space for the three-dimensional Prandtl equations},
  author={Wei-Xi Li, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211210398657573},
  booktitle={arXiv preprint arXiv:1708.08217},
  year={2017},
}
Wei-Xi Li, and Tong Yang. Well-posedness in Gevrey function space for the three-dimensional Prandtl equations. 2017. In arXiv preprint arXiv:1708.08217. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211210398657573.
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