Abstract
AbstractIn this article, we prove that small localized data yield solutions to Kawahara-type equations which have linear dispersive decay on a finite time scale depending on the size of the initial data. We use the similar method used by Ifrim and Tataru to derive the dispersive decay bound of the solutions to the KdV equation, with some steps being simpler. This result is expected to be the first result of the small data global bounds of the fifth-order dispersive equations with quadratic nonlinearity.
Funder
National Research Foundation
Publisher
Springer Science and Business Media LLC
Reference30 articles.
1. Bjoern Bringmann, Rowan Killip, and Monica Visan. “Global well-posedness for the fifth-order KdV equation in $$H^{-1}({mathbb{R}})$$”. arXiv preprintarXiv:1912.01536 (2019).
2. Thierry Cazenave. Semilinear Schrodinger Equations. Vol. 10. American Mathematical Soc., 2003.
3. Wengu Chen and Zihua Guo. “Globalwell-posedness and I method for the fifth order Korteweg-de Vries equation”. Journal d’Analyse Math é matique 114.1 (2011), p. 121.
4. Wengu Chen, Junfeng Li, Changxing Miao, and Jiahong Wu. “Low regularity solutions of two fifth-order KdV type equations”. Journal d’Analyse Math é matique 107.1 (2009), p. 221.
5. Shang Bin Cui, Dong Gao Deng, and Shuang Ping Tao. “Global existence of solutions for the Cauchy problem of the Kawahara equation with $$L^2$$ initial data”. Acta Mathematica Sinica 22.5 (2006), pp. 1457–1466