On the nonexistence of time dependent global weak solutions to the compressible Navier-Stokes equations

2009/01/21 by Dongho Chae, Chae, Dongho
Mathematics · #76N10 #76W05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:76N10 #msc:76W05

paper · pdf · doi:10.48550/arxiv.0901.3278

8 pages(revised and substantially reduced version of the previous one)

arxiv created 2009/06/17 · arxiv updated 2009/12/01

Abstract

In this paper we prove the nonexistence of global weak solutions to the compressible Navier-Stokes equations for the isentropic gas in \Bbb R^N, N≥ 3, where the pressure law given by p(ρ)=aρ^γ, a>0, 1<γ≤ (N)/(4)+\frac12. In this case if the initial data satisfies ∫_{\Bbb R^N} ρ₀ (x)v₀ (x)⋅ x dx >0, then there exists no finite energy global weak solution which satisfies the integrability conditions ρ|x|² ∈ L¹_loc (0, ∞; L¹ (\Bbb R^N)) and v∈ L¹_loc (0, ∞; L^(N)/(N-1) (\Bbb R^N)).

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