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

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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.

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References

  1. 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)

    Article  MATH  MathSciNet  Google Scholar 

  2. 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)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bourgain, J.: On the Cauchy problem for periodic KdV-type equations. J. Fourier Anal. Appl. 17–86 (1995). Kahane Special Issue

  4. 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)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hu, Y., Li, X.: Discrete Fourier restriction associated with Schrödinger equations. Preprint

  6. Hu, Y., Li, X.: Discrete Fourier restriction associated with KdV equations. Preprint

  7. Hua, L.K.: Additive Theory of Prime Numbers. Translations of Math. Monographs, vol. 13. AMS, Providence (1965)

    MATH  Google Scholar 

  8. Montgomery, H.L.: Ten lectures on the interface between analytic number theory and harmonic analysis. CBMS, vol. 84. AMS, Providence (1994)

    MATH  Google Scholar 

  9. Wooley, T.D.: Vinogradov’s mean value theorem via efficient congruence. Ann. of Math. To appear

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Correspondence to Xiaochun Li.

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Communicated by Steven G. Krantz.

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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

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  • DOI: https://doi.org/10.1007/s12220-013-9443-4

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