id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-154	Qin, Liuna; Xiao, Changguo; Zhang, Yinghui	Optimal decay rates for higher-order derivatives of solutions to 3D compressible Navier-Stokes-Poisson equations with external force	2022	18	.pdf	application/pdf	6063	447	82	For T > 0, let (ρ − ρ̃, u, φ − φ̃)(x, t) be a solution of (1.1) in [0, T ] and introduce E(T ) Then there exists δ > 0 such that if E(T ) + ε1 ≤ δ, (1.6) then the following a-priori estimate holds ‖(ρ− ρ̃, u,∇φ−∇φ̃)(·, t)‖2H2 + ∫ t 0 ‖(ρ− ρ̃,∇u,∇2φ−∇2φ̃)(·, s)‖2H2ds ≤ C‖(ρ0 − ρ̃, u0)‖2H2 , (1.7) for any t ∈	cache/ejde-154.pdf	txt/ejde-154.txt