In this paper, we investigate the best profile of the classical solutions for the Euler equations with time‐dependent damping term −α(1+t)λu when v+ = v− and u+=u−=0. Based on the time‐weighted energy method, we deduce that the solutions time‐asymptotically converge to the nonlinear diffusion wave with the special initial data and the improved convergence decay rates which are faster than the previous results obtained by Cui et al. (2018, J. Differential Equations, 264, 4564–4602) and Li et al. (2017, J. Math. Anal. Appl., 456, 849–871).
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