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Global regularity problem of two‐dimensional magnetic Bénard fluid equations
Author(s) -
Ma Liangliang
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7165
Subject(s) - thermal diffusivity , dissipation , laplace operator , mathematics , fractional laplacian , diffusion , magnetic diffusivity , partial differential equation , mathematical analysis , physics , magnetic field , thermodynamics , magnetohydrodynamics , quantum mechanics
In the paper, we devote to broadening the current global regularity results for the two‐dimensional magnetic Bénard fluid equations. We study three cases: (i) fractional Laplacian dissipation (‐ Δ) α u , partial magnetic diffusion ( ∂x 2x 22b 1 , ∂x 1x 12b 2 ) , and Laplacian thermal diffusivity Δ θ ; (ii) partial fractional dissipation ( Λx 22 αu 1 , Λx 12 αu 2 ) , partial magnetic diffusion ( ∂x 2x 22b 1 , ∂x 1x 12b 2 ) , and Laplacian thermal diffusivity Δ θ ; (iii) partial fractional magnetic diffusion ( Λx 22 βb 1 , Λx 12 βb 2 ) , Laplacian thermal diffusivity Δ θ , and without Laplacian dissipation Δ u (i.e., μ = 0 ), and establish the global regularity for each cases.