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

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

2012-02-03

arxiv.org/abs/1202.0718v1

International Mathematics Research Notices (2011) doi:10.1093/imrn/rnr218

Mathematics

Analysis of PDEs

Scientific paper

10.1093/imrn/rnr218

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.

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