Communications in Mathematical Physics

, Volume 271, Issue 2, pp 511–522 | Cite as

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

  • A. Alexandrou Himonas
  • Gerard Misiołek
  • Gustavo Ponce
  • Yong Zhou
Article

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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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • A. Alexandrou Himonas
    • 1
  • Gerard Misiołek
    • 1
  • Gustavo Ponce
    • 2
  • Yong Zhou
    • 3
    • 4
  1. 1.Department of MathematicsUniversity of Notre DameNotre DameUSA
  2. 2.Department of MathematicsUniversity of CaliforniaSanta BarbaraUSA
  3. 3.Department of MathematicsEast China Normal UniversityShangaiChina
  4. 4.Institute des Hautes Éudes ScientifiquesBures-sur-YvetteFrance

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