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Global Solutions to 3D Rotating Boussinesq Equations in Besov Spaces

  • Jinyi SunEmail author
  • Chunlan Liu
  • Minghua Yang
Article
  • 53 Downloads

Abstract

In this paper, the three-dimensional rotating Boussinesq equations are considered. By striking new balances between the regularizing effects of the Laplacian dissipation and the dispersive effects of the Coriolis force, we obtain the global existence of mild solutions to Cauchy problem of the three-dimensional rotating Boussinesq equations. Particularly, the size of the norm of initial velocity can be arbitrarily large, provided that the speed of rotation is sufficiently high.

Keywords

Boussinesq equations Coriolis force Global solutions 

Mathematics Subject Classification

35A01 76U05 35Q35 35Q86 

Notes

Acknowledgements

The authors would like to convey their sincerest thanks to the anonymous reviewer for the insightful comments and suggestions. J. Sun’s work is partial supported by the National Natural Science Foundation of China (Grant No. 11571381), the Natural Science Foundation of Gansu Province for Young Scholars (Grant No. 18JR3RA102), NWNU-LKQN-17-11 and NWNU-LKQN-18-15. M. Yang’s work is partial supported by the National Natural Science Foundation of China (Grant No. 11801236), Postdoctoral Science Foundation of China (Grant No. 2018M632593), Natural Science Foundation of Jiangxi Province for Young Scholars (Grant No. 20181BAB211001), the Postdoctoral Science Foundation of Jiangxi Province (Grant No. 2017KY23) and Educational Commission Science Programm of Jiangxi Province (Grant No. GJJ170345).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsNorthwest Normal UniversityLanzhouPeople’s Republic of China
  2. 2.Department of MathematicsJiangxi University of Finance and EconomicsNanchangPeople’s Republic of China

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