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数学大讲堂

Some recent progress on the mathematical analysis of the Prandtl boundary layer equation

  • 演讲者:徐超江(鲁昂大学)

  • 时间:2018-04-25 16:20-17:20

  • 地点:慧园3栋 415报告厅

In 1904, Prandtl said that, in fluid of small viscosity, the behavior of fluid near the boundary is completely different from that away from the boundary. Away from the boundary part can be almost considered as ideal fluid, but the near boundary part is deeply affected by the viscous force and is described by Prandtl boundary layer equation which was firstly derived formally by Prandtl. From the mathematical point of view, the well-posedness and justification of the Prandtl boundary layer theory don’t have satisfactory theory yet. In this talk, we present some recent progress on the mathematical analysis of the Prandtl boundary layer equation. By using energy method, we study the well-posedness of Cauchy problem and the smoothness effect of solutions for Prandtl equations in Sobolev space.


[1] R. Alexandre, Y. G. Wang, C.-J. Xu and T. Yang :  Well-posedness of the Prandtl  equation in Sobolev spaces, Journal of the Amercican Mathematical Society. 28 (2015) 745-784

[2] W.-X. Li, D. Wu and C.-J. Xu, Gevery class smoothing effect for the Prandtl equation,. SIAM J. Math. Anal. 48 (2016). 1672-1726.

[3] C.-J. Xu and X. Zhang, Long time well-posdness of the Prandtl equations in Sobolev space. J. Differential Equations,. 263 (2017)  8749-8803

[4] W.-X. Li, V.-S. Ngo and C.-J. Xu, Boundary layer analysis for the fast horizontal rotating fluid,  Preprint