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Global well-posedness for the 2D micropolar Bénard fluid system with mixed partial dissipation, angular viscosity and without thermal diffusivity. (English) Zbl 1490.35335

Summary: 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 F. Xu and M. Chi [Appl. Math. Lett. 108, Article ID 106508, 5 p. (2020; Zbl 1450.35098)] on 2D micropolar Bénard system with full dissipation and angular viscosity.

MSC:

35Q35 PDEs in connection with fluid mechanics
76A05 Non-Newtonian fluids
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness

Citations:

Zbl 1450.35098
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References:

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