id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1499	Zhai, Xiaoping	Linear stability of the Couette flow for non-isentropic compressible fluids	2025	14	.pdf	application/pdf	6238	308	73	Integration in x equations in (1.15), one infer that ∂tρ0 = −α0, ∂tα0 = − 1 γM2 ∂yyρ0 − 1 γM2 ∂yyθ0 + ν∂yyα0, ∂tω0 = α0, ∂tθ0 = −(γ − 1)α0. (2.1) From (2.1), we can further get α0 satisfies the damped wave equations ∂ttα0 − ν∂t∂yyα0 − 1 M2 ∂yyα0 = 0, in R, (2.2) and ρ0 + θ0 satisfies the wave equation ∂tt(ρ0 + θ0)− 1 M2 ∂yy(ρ0 + θ0) (2.15) 8 X. ZHAI EJDE-2025/107 From the equations in (2.10) and definitions of Z1 and Z2, a simple computations gives ∂tZ1 = −∂tm m Z1 − 1 4 ∂tp p Z1 − 1 M p1/2Z2, ∂tZ2 = − (∂tm m + νp ) Z2	cache/ejde-1499.pdf	txt/ejde-1499.txt