Global regularity for the micropolar Rayleigh-Bénard problem with only velocity dissipation

Proceedings of the Royal Society of Edinburgh Section A: Mathematics - Tập 152 Số 5 - Trang 1109-1138 - 2022
Lihua Deng1, Haifeng Shang1
1School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, People’s Republic of China

Tóm tắt

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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Proceedings of the Royal Society of Edinburgh Section A: Mathematics

Tập 152 Số 5

1109-1138

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