Asymptotics of Stationary Navier Stokes Equations in Higher Dimensions

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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.

Original languageEnglish (US)
Pages (from-to)598-611
Number of pages14
JournalActa Mathematica Sinica, English Series
Volume34
Issue number4
DOIs
StatePublished - Apr 1 2018

Bibliographical note

Funding Information:
Received August 30, 2017, accepted September 20, 2017 The second author is supported in part by grant DMS (Grant No. 1362467) from the National Science Foundation; the first author is supported in part by DMS (Grant No. 1600779)

Publisher Copyright:
© 2018, 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.

Keywords

  • Navier Stokes equations
  • asymptotics
  • steady states

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