Global regularity for the micropolar Rayleigh-Bénard problem with only velocity dissipation
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This paper is concerned with the global regularity problem on the micropolar Rayleigh-Bénard problem with only velocity dissipation in $\mathbb {R}^{d}$ with $d=2\ or\ 3$ . By fully exploiting the special structure of the system, introducing two combined quantities and using the technique of Littlewood-Paley decomposition, we establish the global regularity of solutions to this system in $\mathbb {R}^{2}$ . Moreover, we obtain the global regularity for fractional hyperviscosity case in $\mathbb {R}^{3}$ by employing various techniques including energy methods, the regularization of generalized heat operators on the Fourier frequency localized functions and logarithmic Sobolev interpolation inequalities.
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1994 ◽
Vol 447
(1931)
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pp. 587-607
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2000 ◽
Vol 7
(2)
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pp. 136-169
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1986 ◽
pp. 188-209
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1983 ◽
Vol 130
(-1)
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pp. 165
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1985 ◽
Vol 158
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pp. 245-268
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2017 ◽
Vol 104
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pp. 438-455
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