Remark on global existence of solutions to the 1D compressible Euler equation with time-dependent damping

2019/09/11 by Yuusuke Sugiyama, Sugiyama, Yuusuke
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1909.05683

openalex publication_date 2019/09/11 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the 1D compressible Euler equation with the damping coefficient λ/(1+t)^μ. Under the assumption that 0≤ μ<1 and λ>0 or μ=1 and λ> 2, we prove that solutions exist globally in time, if initial data are small C¹ perturbation near constant states. In particular, we remove the conditions on the limit lim_{|x| → ∞} (u (0,x), v (0,x)), assumed in previous results.

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