Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation
- First Online:
- Cite this article as:
- Himonas, A.A., Misiołek, G., Ponce, G. et al. Commun. Math. Phys. (2007) 271: 511. doi:10.1007/s00220-006-0172-4
- 197 Views
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.