Acta Mathematica Sinica, English Series

, Volume 34, Issue 6, pp 1015–1027 | Cite as

Global well-posedness for the fifth-order mKdV equation

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Abstract

We prove the global well-posedness for the Cauchy problem of fifth-order modified Korteweg–de Vries equation in Sobolev spaces H s (ℝ) for s > \( - \frac{3}{{22}}\) . The main approach is the “I-method” together with the multilinear multiplier analysis.

Keywords

Fifth-order mKdV equation Bourgain space global well-posedness I-method 

MR(2010) Subject Classification

35Q53 47J35 

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Notes

Acknowledgements

We thank the referees for their time and comments.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiP. R. China

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