The Navier-Stokes Problem in the 21st Century

Pierre Gilles Lemarie-Rieusset

© 2016 - Chapman and Hall/CRC
Published March 8, 2016
Reference - 718 Pages
ISBN 9781466566217 - CAT# K16139

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Features

  • Introduces Navier–Stokes equations in simple contexts, explaining the physical meaning of terms in equations, the history of the equations up to Leray, and basic notions pre-dating functional analysis
  • Systematically includes forcing terms in the theorems
  • Examines problems linked to the behavior of the forces
  • Covers parabolic Morrey spaces and capacitary theory applied to the existence of mild solutions
  • Emphasizes scaling properties of the equations in relation with Morrey spaces
  • Discusses recent variants and approximating processes of the partial regularity result of Caffarelli, Kohn, and Nirenberg for suitable solutions

Summary

Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis

The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics.

The book focuses on incompressible deterministic Navier–Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.

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