Optimal Time Decay Rate for the Compressible Viscoelastic Equations in Critical Spaces

2015/02/22 by Junxiong Jia, Jigen Peng, Jia, Junxiong +1 · 2 citations
Engineering · Mathematics · #35D35 #35Q35 #76N10 #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.1502.06167

openalex publication_date 2015/02/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we are concerned with the convergence rates of the global strong solution to constant equilibrium state for the compressible viscoelastic fluids in the whole space. We combine both analysis about Green's matrix method and energy estimate method to get optimal time decay rate in critical Besov space framework. Our result imply the optimal L²-time decay rate and only need the initial data to be small in critical Besov space which have very low regularity compared with traditional Sobolev space.

Cited by

• Global Regularity to Incompressible Viscoelastic System With a Class of Large Initial Data
• Decay estimates for the compressible viscoelastic equations in an exterior domain

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