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Journal of Nonlinear Science

, Volume 29, Issue 1, pp 207–213 | Cite as

Onsager’s Conjecture on the Energy Conservation for Solutions of Euler Equations in Bounded Domains

  • Quoc-Hung Nguyen
  • Phuoc-Tai NguyenEmail author
Article

Abstract

The Onsager’s conjecture has two parts: conservation of energy, if the exponent is larger than 1 / 3, and the possibility of dissipative Euler solutions, if the exponent is less than or equal to 1 / 3. The paper proves half of the conjecture, the conservation part, in bounded domains.

Keywords

Onsager’s conjecture Energy conservation Euler equation 

Mathematics Subject Classification

35Q31 76B03 

Notes

Acknowledgements

The authors are grateful to Emil Wiedemann for helpful comments. We also would like to thank the anonymous referee for constructive comments which helped to improve the note remarkably.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Faculty of Science, Department of Mathematics and StatisticsMasaryk UniversityBrnoCzech Republic

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