Local Well-Posedness of Periodic Fifth-Order KdV-Type Equations

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• 作者：Yi Hu ; Xiaochun Li
• 关键词：Fifth order dispersive equations ; Local well ; posedness ; 42B20 ; 42B25 ; 46B70 ; 47B38
• 刊名：Journal of Geometric Analysis
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：25
• 期：2
• 页码：709-739
• 全文大小：458 KB
• 参考文献：1. Bourgain, J. (1993) Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. Part I: Schr?dinger equations. Geom. Funct. Anal. 3: pp. 107-156 CrossRef
  2. Bourgain, J. (1993) Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. Part II: The KDV-equations. Geom. Funct. Anal. 3: pp. 209-262 CrossRef
  3. Bourgain, J.: On the Cauchy problem for periodic KdV-type equations. J. Fourier Anal. Appl. 17-6 (1995). Kahane Special Issue
  4. Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T. (2004) Multilinear estimates for periodic KdV equations, and applications. J. Funct. Anal. 211: pp. 173-218 CrossRef
  5. Hu, Y., Li, X.: Discrete Fourier restriction associated with Schr?dinger equations. Preprint
  6. Hu, Y., Li, X.: Discrete Fourier restriction associated with KdV equations. Preprint
  7. Hua, L.K. (1965) Additive Theory of Prime Numbers. AMS, Providence
  8. Montgomery, H.L. (1994) Ten lectures on the interface between analytic number theory and harmonic analysis. AMS, Providence
  9. Wooley, T.D.: Vinogradov’s mean value theorem via efficient congruence. Ann. of Math. To appear
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

In this paper, the local well-posedness of periodic fifth-order dispersive equations with nonlinear term P 1(u)?/em> x u+P 2(u)?/em> x u?/em> x u is established. Here P 1(u) and P 2(u) are polynomials of u. We also get some new Strichartz estimates.