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Numerische Mathematik

, Volume 139, Issue 1, pp 187–245 | Cite as

On the long-time stability of a temporal discretization scheme for the three dimensional viscous primitive equations

  • Chun-Hsiung Hsia
  • Ming-Cheng Shiue
Article

Abstract

In this article, a semi-discretized Euler scheme to solve the three dimensional viscous primitive equations is studied. Based on suitable assumptions on the initial data and forcing terms, the long-time stability of the proposed scheme is proven by showing that the \(H^1\) norm (in space variables) of the solutions is bounded at each time step when the time step satisfies certain smallness condition.

Mathematics Subject Classification

35 65 76 

Notes

Acknowledgements

Chun-Hsiung Hsia and Ming-Cheng Shiue were partially supported by the Ministry of Science and Technology, Taiwan under grant MOST 104-2628-M-002-007-MY3 and MOST 104-2115-M-009-012-MY2 (MOST 106-2115-M-009 -011 -MY2) respectively. The authors would like to thank Professor Jie Shen for his very useful feedbacks when Hsia delivered a talk in the first draft of this research project. The authors also appreciate Professor Roger Temam for his comments and kind supports during Shiue’s visit to ISCAM at Indiana University.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Institute of Applied Mathematical SciencesNational Center for Theoretical Sciences, National Taiwan UniversityTaipeiTaiwan
  2. 2.Department of Applied MathematicsNational Chiao Tung UniversityHsin-ChuTaiwan

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