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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
jliu@phy.duke.edu

Robert L. Pego
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
rpego@andrew.cmu.edu

Yue Pu
Department of Mathematical Sciences and
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
ypu@andrew.cmu.edu

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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