Well-posedness and derivative blow-up for a dispersionless regularized shallow water system
| Autor: | Yue Pu, Jian-Guo Liu, Robert L. Pego |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis General Physics and Astronomy Statistical and Nonlinear Physics Classification of discontinuities 01 natural sciences Shock (mechanics) 010101 applied mathematics Waves and shallow water Mathematics - Analysis of PDEs FOS: Mathematics Gravitational singularity 35B44 35B60 35Q35 76B15 35L67 0101 mathematics Finite time Shallow water equations Mathematical Physics Well posedness Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Nonlinearity. 32:4346-4376 |
| ISSN: | 1361-6544 0951-7715 |
| DOI: | 10.1088/1361-6544/ab2cf1 |
| Popis: | 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. Comment: 28 pages, 1 figure; substantial reorganization, corrected proof of blow-up criteria, new references |
| Databáze: | OpenAIRE |
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