Premium
Global smooth solution to the 2D Boussinesq equations with fractional dissipation
Author(s) -
Ye Zhuan
Publication year - 2017
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.4328
Subject(s) - dissipation , fractional laplacian , mathematics , compressibility , laplace operator , order (exchange) , mathematical analysis , diffusion , boussinesq approximation (buoyancy) , mechanics , physics , heat transfer , thermodynamics , natural convection , finance , rayleigh number , economics
In this paper, we consider the 2D incompressible Boussinesq system with fractional Laplacian dissipation and thermal diffusion. On the basis of the previous works and some new observations, we show that the condition 1 − α < β < min3 − 3 α , α 2 , 3 α 2 + 4 α − 4 8 ( 1 − α )with 0 . 7351 ≈ 10 − 2 105 < α < 1 suffices in order for the solution pair of velocity and temperature to remain smooth for all time. Copyright © 2017 John Wiley & Sons, Ltd.