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Breakdown of the Camassa-Holm equation. (English) Zbl 1052.35130

This is a brief note that deals with the breakdown of the Camassa-Holm equation. An earlier proof regarding the breakdown of this equation, under certain conditions, is pointed out to be faulty at some point; a simple proof dropping some conditions, assumed earlier, is presented, of course using the same formalism.

MSC:

35F20 Nonlinear first-order PDEs
35B40 Asymptotic behavior of solutions to PDEs
35L67 Shocks and singularities for hyperbolic equations
35Q58 Other completely integrable PDE (MSC2000)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction

Keywords:

shock wave
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References:

[1] ; Vorticity and incompressible flow. Cambridge University Press, Cambridge, 2002. · Zbl 0983.76001
[2] Camassa, Phys Rev Lett 71 pp 1661– (1993)
[3] Camassa, Adv Appl Math 31 pp 1– (1994)
[4] McKean, Asian J Math 2 pp 767– (1998) · Zbl 0959.35140 · doi:10.4310/AJM.1998.v2.n4.a10
[5] McKean, Asian J Math 3 (1999)
[6] McKean, Comm Pure Appl Math 61 pp 638– (2003)
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