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In this paper we are interested in the upper bound of the lifespan estimatefor the compressible Euler system with time dependent damping and small initialperturbations. We employ some techniques from the blow-up study of nonlinearwave equations. The novelty consists in the introduction of tools from theOrlicz spaces theory to handle the nonlinear term emerging from the pressure $p\equiv p(\rho)$, which admits different asymptotic behavior for large and smallvalues of $\rho-1$, being $\rho$ the density. Hence we can establish, in highdimensions $n\in\{2,3\}$, unified upper bounds of the lifespan estimatedepending only on the dimension $n$ and on the damping strength, andindependent of the adiabatic index $\gamma>1$. We conjecture our results to beoptimal. The method employed here not only improves the known upper bounds ofthe lifespan for $n\in\{2,3\}$, but has potential application in the study ofrelated problems.

Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques