Optimality of the Decay Estimate of Solutions to the Linearised Curl-Free Compressible Navier-Stokes Equations

2023/03/13 by Tsukasa Iwabuchi, Iwabuchi, Tsukasa, Dáithí Ó hAodha +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Cosmology and Gravitation Theories #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2303.06891

openalex publication_date 2023/03/13 · openalex created_date 2023/03/16 · openalex updated_date 2026/07/28

Abstract

We discuss optimal estimates of solutions to the compressible Navier-Stokes equations in Besov norms. In particular, we consider the estimate of the curl-free part of the solution to the linearised equations, in the homogeneous case. We prove that our estimate is optimal in the L^∞-norm by showing that the norm is bounded from below by the same decay rate.

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