On some Liouville Type Theorems for the Compressible Navier-Stokes Equations

2012/09/17 by Dong Li, Li, Dong, Xinwei Yu +1
Engineering · Mathematics · #Computational Fluid Dynamics and Aerodynamics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #math.AP #msc:35Q35

paper · pdf · doi:10.48550/arxiv.1209.3718

16 pages

arxiv created 2012/09/17 · arxiv updated 2012/09/18

Abstract

We prove several Liouville type results for stationary solutions of the d-dimensional compressible Navier-Stokes equations. In particular, we show that when the dimension d \geqslant 4, the natural requirements ρ∈ L^∞ (\mathbbmR^d), v ∈ H¹ (\mathbbmR^d) suffice to guarantee that the solution is trivial. For dimensions d=2,3, we assume the extra condition v ∈ L^(3d)/(d-1)(\mathbb R^d). This improves a recent result of Chae (2012).

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