Well-posedness and derivative blow-up for a dispersionless regularized shallow water system

讲座时间 Datetime: 

星期五, 2018/12/14 - 从 14:30 到 16:00

地点 Venue: 

海滨红楼6号楼1楼会议室

报告人 Speaker: 

刘建国 教授

单位 Affiliation: 

美国杜克大学

报告摘要 Abstract: 

In this talk I will present some results on the local-time well-posedness and breakdown for solutions for a Green-Naghdi type conservative regularization of the shallow water equations as recently derived by D. Clamond and D. Dutykh. The system is linearly non-dispersive, and
smooth solutions conserve an $H^1$-equivalent energy.
No shock discontinuities can occur, but the system is known to admit weakly singular shock-profile solutions
that dissipate energy.  We identify a class of small-energy
smooth solutions that develop singularities in the first derivatives in finite time. This is a joint work with Bob Pego and Yue Pu of Carnegie Mellon University.