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


Journal Article

© 2019 IOP Publishing Ltd & London Mathematical Society. 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 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.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Pego, RL; Pu, Y

Published Date

  • October 4, 2019

Published In

Volume / Issue

  • 32 / 11

Start / End Page

  • 4346 - 4376

Electronic International Standard Serial Number (EISSN)

  • 1361-6544

International Standard Serial Number (ISSN)

  • 0951-7715

Digital Object Identifier (DOI)

  • 10.1088/1361-6544/ab2cf1

Citation Source

  • Scopus