Breakdown for the Camassa-Holm Equation Using Decay Criteria and Persistence in Weighted Spaces

By Lorenzo Brandolese. 2012

86 citations recorded by the source corpus.

We exhibit a sufficient condition in terms of decay at infinity of the initial data for the finite time blowup of strong solutions to the Camassa--Holm equation: a wave breaking will occur as soon as the initial data decay faster at infinity than the solitons. In the case of data decaying slower than solitons we provide persistence results for the solution in weighted $L^p$-spaces, for a large class of moderate weights. Explicit asymptotic profiles illustrate the optimality of these results.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/01581aadcf4730ccf3a22181457dd4f3bcaa7a17

Citations in the corpus

• Local-in-Space Criteria for Blowup in Shallow Water and Dispersive Rod Equations (2012, unknown): “2), in the case 1 ≤ γ ≤ 4 (for γ 6∈ [1, 4], see Section 4).”