On the fifth order KdV equation: local well-posedness and lack of uniform continuity of the solution map
By Soonsik Kwon. 2007
66 citations recorded by the source corpus.
In this paper we prove that the fifth order equation arising from the KdV hierarchy $ \partial_tu + \partial_x^5u + c_1\partial_x u\partial_x^2u + c_2u\partial_x^3u = 0 $ is locally well-posed in $ H^s(\mathbb{R}) $ for $ s> 5/2. Also, we prove the solution map of the equation is not uniformly continuous for $s>0$.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/95863de0a3e97d4739ae8be0506100c749aa2ce6
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In Applied Mathematics
- Didier Pilod
- Carlos E. Kenig
- Aynur Bulut
- Gunther Uhlmann
- Raphael Cote
- B. Dodson
- Zhongwei Shen
- Luc Molinet
In Mathematical Physics
- Didier Pilod
- Carlos E. Kenig
- Aynur Bulut
- Raphael Cote
- Gunther Uhlmann
- B. Dodson
- Luc Molinet
- F. Merle
In Statistical and Nonlinear Physics
- Carlos E. Kenig
- Didier Pilod
- Justin Holmer
- Andrei V. Faminskii
- F. Merle
- B. Dodson
- Luc Molinet
- A. Alexandrou Himonas
Citations in the corpus
- Well-posedness for the fifth-order KdV equation in the energy space (2012, background): “MR2858525 (2012k:35468) [13] Z. Guo, C. Kwak and S. Kwon, Rough solutions of the fifth-order KdV equations, J. Funct.”