id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-581	Wu, Wanping; Zhang, Yinghui	Global low-energy weak solutions for compressible magneto-micropolar fluids with discontinuous initial data in R^3	2023	33	.pdf	application/pdf	12504	600	82	= sup 1≤s≤t ( ‖∇u‖2L2 + ‖w‖2L2 + ‖∇w‖2L2 + ‖∇H‖2L2 ) + sup 1≤s≤t ( ‖u̇‖2L2 + ‖ẇ‖2L2 + ‖∇W1‖2L2 + ‖∇W2‖2L2 + ‖Ht‖2L2 ) + ∫ t 1 ( ‖u̇‖2L2 + ‖ẇ‖2L2 + ‖∇W1‖2L2 + ‖∇W2‖2L2 + ‖Ht‖2L2 ) ds + ∫ t 1 (‖∇u̇‖2L2 + ‖∇ẇ‖2L2 + ‖∇Ht‖2L2) ds, (3.3) Oq(t) = sup 0≤s≤t (‖u‖qLq + ‖w‖qLq + ‖H‖qLq ) + ∫ t 0 ∫ R3 ( |u|q−2|∇u|2 + |w|q−2|∇w|2 + |H|q−2|∇H|2 ) dxds + ∫ t 0 ∫ R3 ( |u|q−4|∇(|u|2)|2 + |w|q−4|∇(|w|2)|2 + |H|q−4|∇(|H|2)|2 ) Later, to deal with the terms 2ζ ∫ t 0 ∫ R3 ϑ rotw · u̇dx ds and 2ζ ∫ t 0 ∫ R3 ϑ rotu ·ẇ dxds, we use integration by parts to obtain 2ζ ∫ t 0 ∫ R3 ϑ rotw · u̇dxds+ 2ζ ∫ t 0 ∫ R3 ϑ rotu ·	cache/ejde-581.pdf	txt/ejde-581.txt