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On the global regularity of the 2D Boussinesq equations with fractional dissipation
Author(s) -
Ye Zhuan,
Xu Xiaojing,
Xue Liutang
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500413
Subject(s) - mathematics , dissipation , boussinesq approximation (buoyancy) , mathematical analysis , mechanics , physics , thermodynamics , convection , natural convection , rayleigh number
In this paper, we consider the two‐dimensional (2D) incompressible Boussinesq equations with fractional Laplacian dissipation and thermal diffusion. Attention is focused on the subcritical case when the velocity dissipation dominates. More precisely, we establish the global regularity result of the 2D Boussinesq equations in a new range of fractional powers of the Laplacian, namely 1 − α < β < min α 2 ,( 3 α − 2 ) ( α + 2 ) 10 − 7 α ,2 − 2 α 4 α − 3with 0.783 ≈ 21 − 217 8 < α < 1 . Therefore, this result significantly improves the previous work [31][C. Miao, 2011] which obtained the global regularity result for 1 − α < β < f ( α ) with 0.888 ≈ 6 − 6 4 < α < 1 , where f ( α ) < 1 is an explicit function.