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Global well-posedness for the 2D micropolar Bénard fluid system with mixed partial dissipation, angular viscosity and without thermal diffusivity

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Abstract

In this paper, we study the Cauchy problem of the 2D micropolar Bénard system with partial viscosity, i.e., (1) \(\mu _{12}=\mu _{21}=\gamma _{1}=1,\ \mu _{11}=\mu _{22}=\gamma _{2}=\nu _{1}=\nu _{2}=0;\) (2) \(\mu _{12}=\mu _{21}=\gamma _{2}=1,\ \mu _{11}=\mu _{22}=\gamma _{1}=\nu _{1}=\nu _{2}=0,\) where \(\mu _{ij},\ \gamma _{i},\ \nu _{i}\ (i,j=1,2)\) are the coefficients of dissipation, angular viscosity and thermal diffusivity, respectively. This work extends the result of Xu (Appl. Math. Lett. 108(2020)) on 2D micropolar Bénard system with full dissipation and angular viscosity.

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  1. School of Mathematical Sciences, Xiamen University, Xiamen, China

    Xinliang Li & Zhong Tan

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  1. Xinliang Li
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  2. Zhong Tan
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This work was supported by National Natural Science Foundation of China, NSFC (NO: 11926316, 11531010, 12071391).

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Li, X., Tan, Z. Global well-posedness for the 2D micropolar Bénard fluid system with mixed partial dissipation, angular viscosity and without thermal diffusivity. Z. Angew. Math. Phys. 73, 83 (2022). https://doi.org/10.1007/s00033-022-01726-8

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  • DOI: https://doi.org/10.1007/s00033-022-01726-8

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