id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-394	Fang, Yue; Li, Kaiqiang; Xu, Xin	Global classical solutions to equatorial shallow-water equations	2023	16	.pdf	application/pdf	5895	322	77	+ 1 8 ‖ωy‖2. (3.47) Similar derivations show that∫ Ω ωy∇ · U dx ≤ ‖ωy‖‖∇ · U‖ ≤ ‖ωy‖‖U‖1 ≤ C3 ( W (t)3/2 + E(t) + ‖ω‖2 ) + 1 8 ‖ωy‖2. Since ∫ Ω ωttU · ∇ωtt dx = ∫ Ω ∇ · (ω 2 tt 2 U)− ω2 tt 2 ∇ · U dx = − ∫ Ω ω2 tt 2 ∇ · U dx ≤ C3W (t)3/2, (3.56) and∫ Ω yωtt∇ ·	cache/ejde-394.pdf	txt/ejde-394.txt