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

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.

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Acknowledgements

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

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Correspondence to Peipei Shang.

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Dedicated to Philippe G. Ciarlet with admiration and friendship on the occasion of his 80th birthday

This work was supported by the National Natural Science Foundation of China (Nos. 11401021, 11471044, 11771336, 11571257), the LIASFMA, the ANR project Finite4SoS (No.ANR 15-CE23-0007) and the Doctoral Program of Higher Education of China (Nos. 20130006120011, 20130072120008).

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Chu, J., Coron, JM., Shang, P. et al. Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation. Chin. Ann. Math. Ser. B 39, 201–212 (2018). https://doi.org/10.1007/s11401-018-1060-x

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Keywords

  • Korteweg-de Vries equation
  • Resolvent estimation
  • Analytic semigroup
  • Gevrey class

2000 MR Subject Classification

  • 35Q53
  • 35P05
  • 47D03