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The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

In: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Author

Listed:
  • Yasunori Maekawa

    (Graduate School of Sciences, Kyoto University, Department of Mathematics)

  • Anna Mazzucato

    (Eberly College of Science, The Pennsylvania State University, Mathematics Department)

Abstract

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this chapter is to review recent progress on the mathematical analysis of this problem in each category.

Suggested Citation

  • Yasunori Maekawa & Anna Mazzucato, 2018. "The Inviscid Limit and Boundary Layers for Navier-Stokes Flows," Springer Books, in: Yoshikazu Giga & Antonín Novotný (ed.), Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, chapter 15, pages 781-828, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13344-7_15
    DOI: 10.1007/978-3-319-13344-7_15
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