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Chinese Annals of Mathematics, Series B

, Volume 39, Issue 2, pp 201–212 | Cite as

Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation

  • Jixun Chu
  • Jean-Michel Coron
  • Peipei ShangEmail author
  • Shu-Xia Tang
Article

Abstract

In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries (KdV for short) equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup generated by the linear operator is not analytic but of Gevrey class δ ∈ (3/2, ∞) for t > 0.

Keywords

Korteweg-de Vries equation Resolvent estimation Analytic semigroup Gevrey class 

2000 MR Subject Classification

35Q53 35P05 47D03 

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Notes

Acknowledgements

The authors thank Bingyu Zhang for his interesting comments and many valuable suggestions on this work.

References

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jixun Chu
    • 1
  • Jean-Michel Coron
    • 2
    • 3
  • Peipei Shang
    • 4
    • 2
    • 5
    Email author
  • Shu-Xia Tang
    • 6
    • 2
  1. 1.Department of Applied Mathematics, School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingChina
  2. 2.UPMC Univ. Paris 06, UMR 7598, Laboratoire Jacques-Louis LionsSorbonne UniversitésParisFrance
  3. 3.ETH Institut für Theoretische Studien (ETH-ITS)ZürichSwitzerland
  4. 4.School of Mathematical SciencesTongji UniversityShanghaiChina
  5. 5.EHT Institute for Mathematical Research (ETH-FIM)ZürichSwitzerland
  6. 6.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

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