WIAS Preprint No. 3167, (2025)

AT-coercivity approach to the nonlinear Stokes equations



Authors

  • Cárcamo, Cristian
    ORCID: 0000-0002-8260-6764
  • Ciarlet Jr., Patrick

2020 Mathematics Subject Classification

  • 65N30 76S05 74F10

Keywords

  • Nonlinear Stokes, quasi-Newtonian flow, T-coercivity

DOI

10.20347/WIAS.PREPRINT.3167

Abstract

We address the nonlinear Stokes problem with Dirichlet boundary conditions, introducing additional variables into the standard formulation to accommodate solutions with reduced regularity requirements. To ground this analysis, we first review relevant preliminary results, emphasizing the significance of achieving T -coercivity in the context of nonlinear Stokes flows. We then introduce a specially designed operator T , proving its bijectivity and showing that it induces coercivity when applied to the test function space. This result provides a rigorous foundation for solving the quasi- Newtonian Stokes problem with minimal regularity constraint and also sets up the T -coercivity as an alternative to the well-posedness of the nonlinear Stokes problems.

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