Well-posedness and derivative blow-up for a dispersionless regularized shallow water system
Analysis of PDEs
2020-01-08 v2
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 -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.
Keywords
Cite
@article{arxiv.1810.06096,
title = {Well-posedness and derivative blow-up for a dispersionless regularized shallow water system},
author = {Jian-Guo Liu and Robert L. Pego and Yue Pu},
journal= {arXiv preprint arXiv:1810.06096},
year = {2020}
}
Comments
28 pages, 1 figure; substantial reorganization, corrected proof of blow-up criteria, new references