JOURNAL ARTICLE

Solvability of the two-dimensional stationary incompressible inhomogeneous Navier–Stokes equations with variable viscosity coefficient.

  • Published In: Communications in Contemporary Mathematics, 2024, v. 26, n. 7. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: He, Zihui; Liao, Xian 3 of 3

Abstract

We show the existence and the regularity properties of (a class of) weak solutions to the two-dimensional stationary incompressible inhomogeneous Navier–Stokes equations with density-dependent viscosity coefficients, by analyzing a fourth-order nonlinear elliptic equation for the stream function. For some stationary symmetric flows, we reformulate the Navier–Stokes equations as ordinary differential equations and give explicit examples of weak solutions. We present some further (ir-)regularity results in the case of piecewise-constant viscosity coefficients. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Communications in Contemporary Mathematics. 2024/09, Vol. 26, Issue 7, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:0219-1997
  • DOI:10.1142/S0219199723500396
  • Accession Number:177778546
  • Copyright Statement:Copyright of Communications in Contemporary Mathematics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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