High-frequency smooth solutions and well-posedness of the Camassa-Holm equation

By A. Alexandrou Himonas, G. Misiołek. 2005

64 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/90c7d5ef137cfe7ac843995a16ef88364d63d849

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Yong Zhou
2. Carlos E. Kenig
3. A. Alexandrou Himonas
4. G. Misiołek
5. Gustavo Ponce
6. Lorenzo Brandolese
7. Lidiao Ni
8. Zhengguang Guo

In Mathematical Physics

1. A. Alexandrou Himonas
2. Carlos E. Kenig
3. Yong Zhou
4. Gustavo Ponce
5. G. Misiołek
6. Luc Molinet
7. Lorenzo Brandolese
8. Zihua Guo

In Statistical and Nonlinear Physics

1. A. Alexandrou Himonas
2. Yong Zhou
3. Carlos E. Kenig
4. G. Misiołek
5. Gustavo Ponce
6. Lorenzo Brandolese
7. Luc Molinet
8. John Holmes

Citations in the corpus

• Non-uniform dependence on initial data for the CH equation on the line (2009, methodology): “ts at which the slope is 1 (cuspons). Also, in [HMP] the analogues result for the periodic CH was proved. For s2 non-uniform continuity of the CH solution map in the periodic case was established in [HM] using high frequency traveling wave solutions and following an approach similar to the one used ”
• Non-Uniform Dependence for the Periodic CH Equation (2010, methodology): “We consider the periodic Cauchy problem for the Camassa–Holm equation (CH) and show that its solution map is not uniformly continuous for initial data in Sobolev spaces H s (𝕋) with s  > 3/2, thus extending to 3/2  s   12 ] for s  ≥ 2 and in [ 13 ] for s  = 1.”
• Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation (2006, background): “for the Camassa-Holm equation is not locally uniformly continuous in Sobolev spaces can be found in [ HM2 ].”