Convergence rates to the Barenblatt solutions for the compressible Euler equations with time-dependent damping

作者：Cui, Haibo; Yin, Haiyan; Zhu, Changjiang^*

来源：Journal of Differential Equations, 2023, 374: 761-788.

DOI：10.1016/j.jde.2023.08.034

• Compressible Euler equations with time-dependent damping
• Barenblatt solutions
• Decay rates

In this paper, we are concerned with the asymptotic behavior of L infinity weak entropy solutions for the compressible Euler equations with time-dependent damping and vacuum for any large initial data. This model describes the motion for the compressible fluid through a porous medium, and the friction force is time-dependent. We obtain that the density converges to the Barenblatt solution of a well-known porous medium equation with the same finite initial mass in L-1 decay rate when 1+root 5/2 < gamma <= 2, 0 < lambda < gamma(2)-gamma-1/gamma(2)+gamma-1 or gamma >= 2, 0 <= lambda <1/2 gamma+1 which partially improves and extends the previous work [14,6]. The proof is mainly based on the detailed analysis of the relative weak entropy, time-weighted energy estimates and the iterative method.