, Volume 271, Issue 2, pp 511-522
Date: 08 Feb 2007

Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation

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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.

Communicated by P. Constantin