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Persistence Properties and Unique Continuation of solutions of the Camassa-Holm equation

A. Alexandrou Himonas·Gerard Misiołek·Gustavo Ponce·Yong Zhou
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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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A. Alexandrou Himonas, Gerard Misiołek, Gustavo Ponce, Yong Zhou. 2006-04-18. Persistence Properties and Unique Continuation of solutions of the Camassa-Holm equation. https://arxiv.org/abs/math/0604192

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