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      Stability of two-dimensional solutions to the Navier-Stokes equations in cylindrical domains under Navier-boundary conditions

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          Abstract

          The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time. Assuming that the initial velocity and the external force are sufficiently close to the initial velocity and the external force of the two-dimensional solutions we prove global existence of three-dimensional solutions which remain close to the two-dimensional solutions for all time. In this way we mean stability of two-dimensional solutions.

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          Author and article information

          Journal
          14 October 2015
          Article
          1510.04002
          4a03fe30-15d8-49c4-96b7-1ab282ae04fd

          http://creativecommons.org/publicdomain/zero/1.0/

          History
          Custom metadata
          35Q30, 76D03, 76D05, 76N10, 35B35
          28 pages. arXiv admin note: text overlap with arXiv:1406.0693
          math.AP

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