Abstract In this paper, we consider the non-isentropic compressible Euler equations with time-dependent damping − α (t) u in one space dimension v t − u x = 0, u t + p (v, s) x = − α (t) u, s t = 0. casesₓ-uₗ=0, \\ uₓ+p (v, s) ₗ=- (t) u, \\ sₓ=0. cases Under some conditions on the initial data and the entropy function, we prove some existence theorems of global smooth solutions for the Cauchy problem. At present, there seems to be no research on this kind of problem.
Sui et al. (Thu,) studied this question.