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Acta Mathematica Sinica, English Series

, Volume 34, Issue 4, pp 598–611 | Cite as

Asymptotics of Stationary Navier Stokes Equations in Higher Dimensions

  • Hao Jia
  • Vladimír Šverák
Article
  • 94 Downloads

Abstract

We show that the asymptotics of solutions to stationary Navier Stokes equations in 4, 5 or 6 dimensions in the whole space with a smooth compactly supported forcing are given by the linear Stokes equation. We do not need to assume any smallness condition. The result is in contrast to three dimensions, where the asymptotics for steady states are different from the linear Stokes equation, even for small data, while the large data case presents an open problem. The case of dimension n = 2 is still harder.

Keywords

Navier Stokes equations steady states asymptotics 

MR(2010) Subject Classification

35B40 35Q30 

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© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MinnesotaMinneapolisUSA

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