Abstract
In this paper, the local well-posedness of periodic fifth-order dispersive equations with nonlinear term P 1(u)∂ x u+P 2(u)∂ x u∂ x u is established. Here P 1(u) and P 2(u) are polynomials of u. We also get some new Strichartz estimates.
Similar content being viewed by others
References
Bourgain, J.: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. Part I: Schrödinger equations. Geom. Funct. Anal. 3(2), 107–156 (1993)
Bourgain, J.: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. Part II: The KDV-equations. Geom. Funct. Anal. 3(3), 209–262 (1993)
Bourgain, J.: On the Cauchy problem for periodic KdV-type equations. J. Fourier Anal. Appl. 17–86 (1995). Kahane Special Issue
Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T.: Multilinear estimates for periodic KdV equations, and applications. J. Funct. Anal. 211, 173–218 (2004)
Hu, Y., Li, X.: Discrete Fourier restriction associated with Schrödinger equations. Preprint
Hu, Y., Li, X.: Discrete Fourier restriction associated with KdV equations. Preprint
Hua, L.K.: Additive Theory of Prime Numbers. Translations of Math. Monographs, vol. 13. AMS, Providence (1965)
Montgomery, H.L.: Ten lectures on the interface between analytic number theory and harmonic analysis. CBMS, vol. 84. AMS, Providence (1994)
Wooley, T.D.: Vinogradov’s mean value theorem via efficient congruence. Ann. of Math. To appear
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Steven G. Krantz.
Rights and permissions
About this article
Cite this article
Hu, Y., Li, X. Local Well-Posedness of Periodic Fifth-Order KdV-Type Equations. J Geom Anal 25, 709–739 (2015). https://doi.org/10.1007/s12220-013-9443-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12220-013-9443-4