On Well-Posedness Results for Camassa-Holm Equation on the Line: A Survey
By Luc Molinet. 2004
116 citations recorded by the source corpus.
Abstract We survey recent results on well-posedness, blow-up phenomena, lifespan and global existence for the Camassa-Holm equation. Results on weak solutions are also considered.
Subfields: Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e26b8010090acc0cb2f8b38d3eb4bb9764152802
How researchers see this paper
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In Geometry and Topology
- Yong Zhou
- Zhaoyang Yin
- Lorenzo Brandolese
- A. Alexandrou Himonas
- Joachim Escher
- David Lannes
- G. Misiołek
- Yue Liu
In Statistical and Nonlinear Physics
- Yong Zhou
- Lorenzo Brandolese
- Yue Liu
- A. Alexandrou Himonas
- Zhaoyang Yin
- Joachim Escher
- G. Misiołek
- Luc Molinet
Citations in the corpus
- Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation (2006, background): “Other blow up results are discussed in [ Mo ].”
- Blow-up of solutions to a nonlinear dispersive rod equation (2006, background): “Using the solitons, it can be easily seen that the Camassa-Holm equation does not make sense in H s for s 20 ]).”
- Blow-up of solutions to the DGH equation (2007, unknown): “For the initial data with lower regularity, we refer to Molinet’s paper [30] and also the recent paper [4].”
- The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations (2007, result): “In contrast to this, both (8) and (9) admit breaking waves in the sense of Definition 3 cf. [6, 9, 27, 28 ] for (8) and [16] for (9).”
- Local-in-Space Criteria for Blowup in Shallow Water and Dispersive Rod Equations (2012, background): “Useful survey papers on such equation are [9] and [26].”
- Stability of multipeakons (2008, background): “…+ 2uxuxx + uuxxx, (t, x) ∈ IR2, (1) can be derived as a model for the propagation of unidirectional shalow water waves over a flat bottom by writing the Green-Naghdi equations in LiePoisson Hamiltonian form and then making an asymptotic expansion which keeps the Hamiltonian structure ([3], [19]).”
- Initial Boundary Value Problems of the Camassa–Holm Equation (2008, background): “(2.6), ũ t x ∈ C 0 T H1 ∩ L 0 T W 1 1 with ũ0 as initial data (Danchin, 2001; Molinet, 2004).”
- Breakdown for the Camassa-Holm Equation Using Decay Criteria and Persistence in Weighted Spaces (2012, background): “Several criteria can be given in order to establish whether or not an initially smooth solution develops a singularity after some time.”