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

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...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 72; no. 1
Main Authors Xu, Fuyi, Qiao, Liening, Zhang, Mingxue
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2021
Springer Nature B.V
Subjects
Cauchy problems
Engineering
Mathematical Methods in Physics
Micropolar fluids
Temperature distribution
Theoretical and Applied Mechanics
Two dimensional models
Well posed problems
Blow-up criterion
Smooth solution
Micropolar Rayleigh–Bénard convection problem
Global regularity
35B45
75B03
Local well-posedness
35B65
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Summary: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.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-020-01454-x