Liouville type theorems on the steady Navier-Stokes equations in R3

Content Provider	Semantic Scholar
Author	Xin, Zhouping Xu, Deliang
Copyright Year	2017
Abstract	In this paper we study the Liouville type properties for solutions to the steady incompressible Navier-Stoks equations in $\mathbf{R}^{3}$. It is shown that any solution to the steady Navier-Stokes equations in $\mathbf{R}^{3}$ with finite Dirichlet integral and vanishing velocity field at far fields must be trivial. This solves an open problem. The key ingredients of the proof include a Hodge decomposition of the energy-flux and the observation that the square of the deformation matrix lies in the local Hardy space. As a by-product, we also obtain a Liouville type theorem for the steady density-dependent Navier-Stokes equations.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://arxiv.org/pdf/1710.06569v2.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article