id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1298	Hong, Hakho	Local solutions for a Brinkman equation coupled with heat-convective and concentration-diffusive equations and a volumetric mass source	2025	18	.pdf	application/pdf	6223	262	78	Assume (1.3), (1.4) and Q0(w̄, θ̄) = 0, S(w̄, θ̄) = 0, Q1(w̄, θ̄) = 0. (1.9) 4 H. HONG EJDE-2025/23 Suppose that the initial data ρ0,u0, φi0 satisfy (ρ0 − ρ̄,u0,w0 − w̄, θ0 − θ̄) ∈ HN (R3), inf x∈R3 ρ0(x) > 0, inf x∈R3 w0(x) > 0, inf x∈R3 θ0(x) > 0 (1.10) for an integer N ≥ 3. (1.16) Setting φ = ρ− ρ̄, m = w − w̄, ζ = θ − θ̄, and using assumption (1.9), we rewrite system (1.1)1, (1.15)1, (1.1)3, (1.16) as follows: φt + ρ̄divu+ u · ∇φ−∇wQ0(w̄, θ̄) ·m−Q′ 0θ(w̄, θ̄)ζ = G1(φ,u,m, ζ), ut − µ ρ̄ ∆u− µ+ λ ρ̄ ∇divu+ 1 αρ̄ u+ Pρ(ρ̄, θ̄; w̄) ρ̄ ∇φ + Pθ(ρ̄, θ̄; w̄) ρ̄ ∇ζ + n∑ i=1 Pwi(ρ̄, θ̄; w̄) ρ̄ ∇mi = G2(φ,u,m, ζ), mt − df∆m+ w̄ divu−DwS(w̄, θ̄)m− S′ θ(w̄, θ̄)ζ = G3(φ,u,m, ζ), ζt + θ̄Pθ(ρ̄, θ̄; w̄) ρ̄eθ(ρ̄, θ̄) divu = κ ρ̄eθ(ρ̄, θ̄) ∆ζ + ∇wQ1(w̄, θ̄) ·m+Q′ 1θ(w̄, θ̄)ζ ρ̄eθ(ρ̄, θ̄) + e(ρ̄, θ̄) ρ̄eθ(ρ̄, θ̄) ( ∇wQ0(w̄, θ̄) ·m+Q′ 0θ(w̄, θ̄)ζ )	cache/ejde-1298.pdf	txt/ejde-1298.txt