On the asymptotic behavior of solutions to the Benjamin-Ono equation
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- by Claudio Muñoz and Gustavo Ponce PDF
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Abstract:
We prove that the limit infimum, as time $t$ goes to infinity, of any uniformly bounded in time $H^1\cap L^1$ solution to the Benjamin-Ono equation converge to zero locally in an increasing in time region of space of order $t/\log t$. Also for a solution with a mild $L^1$-norm growth in time, its limit infimum must converge to zero, as time goes to infinity, locally in an increasing on time region of space of order depending of the rate of growth of its $L^1$-norm. In particular, we discard the existence of breathers and other solutions for the BO model moving with a speed “slower” than a soliton.References
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Additional Information
- Claudio Muñoz
- Affiliation: CNRS and Departamento de Ingeniería Matemática DIM-CMM UMI 2807-CNRS, Universidad de Chile, Santiago, Chile
- MR Author ID: 806855
- Email: cmunoz@dim.uchile.cl
- Gustavo Ponce
- Affiliation: Department of Mathematics, University of California-Santa Barbara, Santa Barbara, California 93106
- MR Author ID: 204988
- Email: ponce@math.ucsb.edu
- Received by editor(s): October 4, 2018
- Received by editor(s) in revised form: March 27, 2019
- Published electronically: June 10, 2019
- Communicated by: Catherine Sulem
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 5303-5312
- MSC (2010): Primary 37K15, 35Q53; Secondary 35Q51, 37K10
- DOI: https://doi.org/10.1090/proc/14643
- MathSciNet review: 4021089