id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-422	Fan, Xiaoting; Wang, Shu; Xu, Wen-Qing	Initial-boundary layer associated with the 3-D Boussinesq system for Rayleigh-Benard convection	2020	20	.pdf	application/pdf	7970	402	79	= T 0 0 , (4.13) where the remainders are RεIn,u = − ∞∑ i=1 ( √ ε)i(ε[∂tu In,i + i∑ j=0 uIn,j · ∇uIn,i−j ] +∇pIn,i + 1 Ek e3 × uIn,i −∆uIn,i −Rae3T In,i), and RεIn,T = − ∞∑ i=1 ( √ ε)i ( ∂tT In,i + i∑ j=0 uIn,j · ∇T It follows from the divergence formula, divergence theorem, (4.46) and the bound- ary condition (4.48) that J5 = − ∫ X uεa · ∇ ( (T εe )2 2 ) dx dy dz = − ∫ X ∇ · ( uεa (T εe )2 2 )	cache/ejde-422.pdf	txt/ejde-422.txt