id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-514	Manna, Utpal; Ashirbad Panda, Akash	Local existence and blow-up criterion for the two and three dimensional ideal magnetic Benard problem	2020	26	.pdf	application/pdf	10077	549	81	For R′ > R, using the property of Fourier truncation operator provided 0 < ε < s− 1, the first term of (3.19) becomes∣∣∣((SR − SR′)[(uR · ∇)uR],uR − uR ′)∣∣∣ ≤ ‖(SR − SR′)[(uR · ∇)uR]‖L2 σ ‖uR − uR ′ ‖L2 σ ≤ C Rε ‖(uR · ∇)uR‖Hεσ‖u R − uR ′ ‖L2 σ = C Rε ‖∇ · (uR ⊗ uR)‖Hεσ‖u R − uR ′ ‖L2 σ ≤ C Rε ‖uR ⊗ uR‖Hsσ‖u R − uR ′ ‖L2 σ ≤ C Rε ‖uR‖2Hsσ‖u R − uR ′ ‖L2 σ . (3.20) ∇)uR],uR − uR ′ ) + ( SR′ [(uR ′ · ∇)(uR − uR ′ )],uR − uR ′ ) .	cache/ejde-514.pdf	txt/ejde-514.txt