Well-posedness and derivative blow-up for a dispersionless regularized shallow water system
Publication
, Journal Article
Liu, JG; Pego, RL; Pu, Y
Published in: Nonlinearity
October 4, 2019
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.
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Published In
Nonlinearity
DOI
EISSN
1361-6544
ISSN
0951-7715
Publication Date
October 4, 2019
Volume
32
Issue
11
Start / End Page
4346 / 4376
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
Citation
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Liu, J. G., Pego, R. L., & Pu, Y. (2019). Well-posedness and derivative blow-up for a dispersionless regularized shallow water system. Nonlinearity, 32(11), 4346–4376. https://doi.org/10.1088/1361-6544/ab2cf1
Liu, J. G., R. L. Pego, and Y. Pu. “Well-posedness and derivative blow-up for a dispersionless regularized shallow water system.” Nonlinearity 32, no. 11 (October 4, 2019): 4346–76. https://doi.org/10.1088/1361-6544/ab2cf1.
Liu JG, Pego RL, Pu Y. Well-posedness and derivative blow-up for a dispersionless regularized shallow water system. Nonlinearity. 2019 Oct 4;32(11):4346–76.
Liu, J. G., et al. “Well-posedness and derivative blow-up for a dispersionless regularized shallow water system.” Nonlinearity, vol. 32, no. 11, Oct. 2019, pp. 4346–76. Scopus, doi:10.1088/1361-6544/ab2cf1.
Liu JG, Pego RL, Pu Y. Well-posedness and derivative blow-up for a dispersionless regularized shallow water system. Nonlinearity. 2019 Oct 4;32(11):4346–4376.
Published In
Nonlinearity
DOI
EISSN
1361-6544
ISSN
0951-7715
Publication Date
October 4, 2019
Volume
32
Issue
11
Start / End Page
4346 / 4376
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics