id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1144	Xing, Zhaojun	Single-component regularity criterion and inviscid limit for axially symmetric MHD-Boussinesq systems	2025	15	.pdf	application/pdf	6851	408	82	∥pLp + ∫ t 0 ∫ R3 |∇H(s, x)|2|H(s, x)|p−2 dx ds ≤ ∥H0∥pLp , ∥H(t, ·)∥L∞ ≤ ∥H0∥L∞ , ∥ρ(t, ·)∥pLp + ∫ t 0 ∫ R3 |∇ρ(s, x)|2|ρ(s, x)|p−2 dx ds ≤ ∥ρ0∥pLp , ∥ρ(t, ·)∥L∞ ≤ ∥ρ0∥L∞ . (3.1) (ii) for (u0, h0, ρ0) ∈ L2 and t ∈ R+, ∥(u, h)(t, ·)∥2L2 + ∫ t 0 ∥∇h (s, ·) ∥2L2 ds ≤ C0(1 + t)2, (3.2) where C0 depends only on ∥(u0, h0, ρ0)∥L2 . Proof. This ends up with ∥∇H(t, ·)∥2L2 + ∫ t 0 ∥∇2H(s, ·)∥2L2 ds ≲ ∥∇H0∥2L2 + ∫ t 0 ∥Ω(s, ·)∥2L2∩L6∥∇h(s, ·)∥2L2 ds. (3.6) Then, we obtain the estimate of N .	cache/ejde-1144.pdf	txt/ejde-1144.txt