Optimal decay for the full compressible Navier-Stokes system in critical L^p Besov spaces

2019/07/26 by Qunyi Bie, Qiru Wang, Bie, Qunyi +3
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.1907.12533

openalex publication_date 2019/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Danchin and He (Math. Ann. 64: 1-38, 2016) recently established the global existence in critical L^p-type regularity framework for the N-dimensional (N≥ 3) non-isentropic compressible Navier-Stokes equations. The purpose of this paper is to further investigate the large time behavior of solutions constructed by them. More precisely, we prove that if the initial data at the low frequencies additionally belong to some Besov space B_2,∞^-σ₁ with σ₁∈ (2-N/2, 2N/p-N/2], then the B_p,1^s norm of the critical global solutions exhibits the optimal decay (1+t)^{-(N)/(2)((1)/(2)-(1)/(p))-(s+σ₁)/(2)} for suitable p and s. The main tool we use is the pure energy argument without the spectral analysis, which enables us to remove the smallness assumption of initial data at the low-frequency.

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