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Global existence for the periodic dispersive Hunter–Saxton equation

  • Weikui Ye
  • Zhaoyang YinEmail author
Article
  • 29 Downloads

Abstract

In this paper, we study an integrable dispersive Hunter–Saxton equation in periodic domain. Firstly, we establish the local well-posedness of the Cauchy problem of the equation in \(H^s ({\mathbb {S}}), s \ge 2,\) by applying the Kato method. Then, based on a sign-preserve property, we obtain a global existence result for the equation. Moreover, we extend the obtained result to some periodic nonlinear partial differential equations of second order of the general form.

Keywords

The periodic dispersive Hunter–Saxton equation Local well-posedness The Kato method Global existence 

Mathematics Subject Classification

35A01 35L03 35L05 35L60 

Notes

Acknowledgements

This work was partially supported by NNSFC (No. 11671407), FDCT (No. 0091/2018/A3), Guangdong Special Support Program (No. 8-2015) and the key Project of NSF of Guangdong Province (No. 2016A030311004). The authors thank the referee for valuable comments and suggestions.

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsSun Yat-sen UniversityGuangzhouChina
  2. 2.Faculty of Information TechnologyMacau University of Science and TechnologyTaipaChina

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