On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations

• Watanabe Yoshitaka

  Research Institute for Information Technology, Kyushu University

• Nakao Mitsuhiro T.

  Faculty of Science and Engineering, Waseda University

• Nagatou Kaori

  Institut für Analysis, Karlsruher Institut für Technologie

Abstract

A compactness proof of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations is presented. The compactness of the operator provides important information for fixed-point formulations, especially for computer-assisted proofs based on Schauder's fixed-point theorem. Our idea for the compactness proof comes from books by Girault & Raviart and Ladyzhenskaia, and our principle would be also applied to convex polygonal regions.

Journal

• JSIAM Letters

  JSIAM Letters 9 (0), 77-80, 2017

  The Japan Society for Industrial and Applied Mathematics

Keywords

• compactness
• nonlinear operator
• Navier-Stokes equation

Details

• CRID: 1390001205299382656
• NII Article ID: 130006252917
• DOI: 10.14495/jsiaml.9.77
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/9/0/9_77/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed