KMS Of Academy of mathematics and systems sciences, CAS
| The Cauchy Problem and Multi-peakons for the mCH-Novikov-CH Equation with Quadratic and Cubic Nonlinearities | |
| Qin, Guoquan1,2; Yan, Zhenya2,3; Guo, Boling4 | |
| 2022-01-16 | |
| Source Publication | JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
 |
| ISSN | 1040-7294 |
| Pages | 60 |
| Abstract | This paper investigates the Cauchy problem of a generalized Camassa-Holm equation with quadratic and cubic nonlinearities (alias the mCH-Novikov-CH equation), which is a generalization of some special equations such as the Camassa-Holm (CH) equation, the modified CH (mCH) equation (alias the Fokas-Olver-Rosenau-Qiao equation), the Novikov equation, the CH-mCH equation, the mCH-Novikov equation, and the CH-Novikov equation. We first show the local well-posedness for the strong solutions of the mCH-Novikov-CH equation in Besov spaces by means of the Littlewood-Paley theory and the transport equations theory. Then, the Holder continuity of the data-to-solution map to this equation are exhibited in some Sobolev spaces. After providing the blow-up criterion and the precise blow-up quantity in light of the Moser-type estimate in the Sobolev spaces, we then trace a portion and the whole of the precise blow-up quantity, respectively, along the characteristics associated with this equation, and obtain two kinds of sufficient conditions on the gradient of the initial data to guarantee the occurance of the wave-breaking phenomenon. Finally, the non-periodic and periodic peakon and multi-peakon solutions for this equation are also explored. |
| Keyword | mCH-Novikov-CH equation Wave breaking Local well-posedness Holder continuity Non-periodic and periodic peakon and multi-peakon solutions |
| DOI | 10.1007/s10884-021-10115-0 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | NSF of China[11925108] ; NSF of China[11731014] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000742792500003 |
| Publisher | SPRINGER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59869 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Yan, Zhenya |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Natl Ctr Math & Interdisciplinary Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mech, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Inst Appl Phys & Computat Math, Beijing 100088, Peoples R China |
| Recommended Citation GB/T 7714 | Qin, Guoquan,Yan, Zhenya,Guo, Boling. The Cauchy Problem and Multi-peakons for the mCH-Novikov-CH Equation with Quadratic and Cubic Nonlinearities[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,2022:60. |
| APA | Qin, Guoquan,Yan, Zhenya,&Guo, Boling.(2022).The Cauchy Problem and Multi-peakons for the mCH-Novikov-CH Equation with Quadratic and Cubic Nonlinearities.JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS,60. |
| MLA | Qin, Guoquan,et al."The Cauchy Problem and Multi-peakons for the mCH-Novikov-CH Equation with Quadratic and Cubic Nonlinearities".JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS (2022):60. |
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