id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-72	Ye, Qin; Zhang, Yinghui	Space-time decay rates of a two-phase flow model with magnetic field in R^3	2023	29	.pdf	application/pdf	10490	612	86	Let (ρ− ρ̄, u, n− n̄, v, B) be the strong solution to the system (1.1)- (1.2) with initial data (ρ0 − ρ̄, u0, n0 − n̄, v0, B0) belonging to the Schwartz class S. Under the assumptions in Theorem 1.1, then there exists a large enough T such that ‖∇k(u− v)(t)‖L2 γ ≤ C(1 + t)− 5 4− k 2+γ , (1.15) EJDE-2023/41 SPACE-TIME DECAY RATES 7 for all t > T , 0 ≤ k ≤ `− 2 and γ ≥ 0, where C is a positive constant independent of t. Now, let us outline the strategies for proving Theorem 1.1 and 1.4, and explain the main difficulties in the process. γ−1 γ , (1.16) for t is large enough and γ > 3 2 , where E(t) := ‖(m,u, σ, v,B)‖2L2 γ and C0, C1, C2 are positive constants independent of t. Applying Lemma 2.5 for (1.16) and the interpolation trick, we show that the Theorem 1.1 holds for case k = 0.	cache/ejde-72.pdf	txt/ejde-72.txt