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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 197, Issue 6, pp 1799–1819 | Cite as

Global-in-time existence results for the two-dimensional Hasegawa–Wakatani equations

  • Shintaro Kondo
Article

Abstract

In order to describe the resistive drift wave turbulence appearing in nuclear fusion plasma, the Hasegawa–Wakatani (HW) equations were proposed in 1983. We consider the two-dimensional HW equations, which have numerous structures (that is, they explain the branching phenomenon in turbulent and zonal flow in a two-dimensional plasma) and the generalized HW equations that include temperature fluctuation. We prove the global-in-time existence of a unique strong solution to both the HW equations and the generalized HW equations in a two-dimensional domain with double periodic boundary conditions.

Keywords

Hasegawa–Wakatani equations Drift wave turbulence Zonal flow Sobolev–Slobodetskiĭ spaces 

Mathematics Subject Classification

Primary 76W05 Secondary 35K45 35Q60 82D10 

Notes

Acknowledgements

The author would like to thank Professor Ryusuke Numata of Hyogo University in Japan for his valuable comments. The present study is partially supported by a Grant-in-Aid for Young Scientists (B) (No. 16K17632) from the Japan Society for the Promotion of Science.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical, Electronic and Computer EngineeringGifu UniversityGifu CityJapan

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