Abstract
It is shown that a strong solution of the Camassa-Holm equation, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if it also decays exponentially at a later time. In particular, a strong solution of the Cauchy problem with compact initial profile can not be compactly supported at any later time unless it is the zero solution.
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Himonas, A.A., Misiołek, G., Ponce, G. et al. Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation. Commun. Math. Phys. 271, 511–522 (2007). https://doi.org/10.1007/s00220-006-0172-4
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DOI: https://doi.org/10.1007/s00220-006-0172-4