Global existence of solutions to 1-d Euler equations with time-dependent damping

In this paper, we study the 1-d isentropic Euler equations with time-dependent damping. Our damping decays at a speed of order −1−1 with respect to time which is a little weaker than the linear one. Under our assumption, we will prove the global existence of solutions to the Euler system and obtain L2L2 and L∞L∞ estimates for the solutions. Our approach is based on some detailed energy estimates.