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Publication 18-CNA-023

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

Jian-Guo Liu
Departments of Physics and Mathematics
Duke University
Durham, NC 27708

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

Yue Pu
Department of Mathematical Sciences and
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213

Abstract: We study local-time well-posedness and breakdown for solutions of regularized Saint-Venant equations (regularized classical shallow water equations) recently introduced by Clamond and Dutykh. The system is linearly non-dispersive, and smooth solutions conserve an H1-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.

Get the paper in its entirety as  18-CNA-023.pdf

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