Well-Posedness and Exponential Decay for the Navier-Stokes Equations of Viscous Compressible Heat-Conductive Fluids with Vacuum

2021/03/30 by Suhua Lai, Hao Xu, Lai, Suhua +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2103.16332

openalex publication_date 2021/03/30 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids with far-field vacuum at infinity in \R³. For less regular data and weaker compatibility condition than those proposed by Cho-Kim \citeCK2006, we first prove the existence of local-in-time solutions belonging to a larger class of functions in which the uniqueness can be shown to hold. The local solution is in fact a classical one away from the initial time, provided the initial density is regular. We also establish the global well-posedness of classical solutions with large oscillations and vacuum in the case when the initial total energy is suitably small. The exponential decay estimates of the global solutions are obtained.

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