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

Abstract In this paper, we study the 1-d isentropic Euler equations with time-dependent damping. Our damping decays at a speed of order − 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 L 2 and L ∞ estimates for the solutions. Our approach is based on some detailed energy estimates.

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