On the well-posedness for the 2D micropolar Rayleigh–Bénard convection problem

Abstract

The article is devoted to the study of Cauchy problem to the Rayleigh–Bénard convection model for the micropolar fluid in two dimensions. We first prove the unique local solvability of smooth solution to the system when the system has only velocity dissipation, and then establish a criterion for the breakdown of smooth solutions imposed only the maximum norm of the gradient of scalar temperature field. Finally, we show the global regularity of the system with zero angular viscosity.

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Correspondence to Fuyi Xu.

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Research supported by the National Natural Science Foundation of China (11501332, 11771043, 51976112), the Natural Science Foundation of Shandong Province (ZR2015AL007), and Young Scholars Research Fund of Shandong University of Technology.

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Xu, F., Qiao, L. & Zhang, M. On the well-posedness for the 2D micropolar Rayleigh–Bénard convection problem. Z. Angew. Math. Phys. 72, 17 (2021). https://doi.org/10.1007/s00033-020-01454-x

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Keywords

  • Local well-posedness
  • Micropolar Rayleigh–Bénard convection problem
  • Blow-up criterion
  • Smooth solution
  • Global regularity

Mathematics Subject Classification

  • 75B03
  • 35B45
  • 35B65