The existence theorem for the steady Navier–Stokes problem in exterior axially symmetric 3D domains

Mikhail Korobkov, Konstantin Pileckas, Remigio Russo

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study the nonhomogeneous boundary value problem for the Navier–Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional exterior domain with multiply connected boundary. We prove that this problem has a solution for axially symmetric domains and data (without any smallness restrictions on the fluxes). Our main tool is a recent version of the Morse–Sard theorem for Sobolev functions obtained by Bourgain et al. (Rev Mat Iberoam 29(1):1–23, 2013).

Original languageEnglish
Pages (from-to)727-784
Number of pages58
JournalMathematische Annalen
Volume370
Issue number1-2
DOIs
Publication statusPublished - 1 Feb 2018

Keywords

  • 35Q30
  • 76D03
  • 76D05

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