On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum

2019/05/27 by Xiangdi Huang, Huang, Xiangdi · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1905.11809

openalex publication_date 2019/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the local well-posedness of strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with density containing vacuum initially. We first prove the local existence and uniqueness of the strong solutions, where the initial compatibility condition proposed in \citecho1,K2,coi1 is removed under suitable sense. Then, the continuous of strong solutions on the initial data is derived under an additional compatibility condition. Moreover, for the initial data satisfying some additional regularity and compatibility condition, the strong solution is proved to be a classical one.

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