On the Liouville type theorem for stationary compressible Navier-Stokes-Poisson equations in \Bbb R^N

2011/06/08 by Dongho Chae, Chae, Dongho
Mathematics · #35Q35 #76N10 #76N15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP #msc:35Q35 #msc:76N10 #msc:76N15

paper · pdf · doi:10.48550/arxiv.1106.1515

8 pages

openalex publication_date 2011/06/08 · arxiv created 2011/06/19 · arxiv updated 2011/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove Liouville type result for the stationary solutions to the compressible Navier-Stokes-Poisson equations(NSP) and the compressible Navier-Stokes equations(NS) in \Bbb R^N, N≥ 2. Assuming suitable integrability and the uniform boundedness conditions for the solutions we are led to the conclusion that v=0. In the case of (NS) we deduce that the similar integrability conditions imply v=0 and ρ=constant on \Bbb R^N. This shows that if we impose the the non-vacuum boundary condition at spatial infinity for (NS), v→ 0 and ρ→ ρ_∞ >0, then v=0, ρ=ρ_∞ are the solutions.

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