Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations

2023/12/08 by Tsukasa Iwabuchi, Iwabuchi, Tsukasa, Dáithí Ó hAodha +1
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.2312.04811

openalex publication_date 2023/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay estimate of the norm of the nonlinear part of the solution. This allows us to obtain a bound from below for the time-decay of the solution in L^∞, proving that our decay estimate in that space is sharp. The decay rate is the same as that of the linear problem for curl-free flow. We also obtain an estimate for a scalar system related to curl-free solutions to the compressible Navier-Stokes equations in a weighted Lebesgue space.

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