Navier–Stokes Equations

An Introduction with Applications

  • Grzegorz Łukaszewicz
  • Piotr Kalita

Part of the Advances in Mechanics and Mathematics book series (AMMA)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 1-9
  3. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 11-37
  4. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 39-81
  5. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 83-93
  6. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 95-110
  7. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 111-142
  8. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 143-167
  9. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 169-181
  10. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 183-205
  11. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 207-250
  12. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 251-275
  13. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 277-295
  14. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 297-316
  15. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 317-336
  16. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 337-357
  17. Grzegorz Łukaszewicz, Piotr Kalita
    Pages 359-376
  18. Back Matter
    Pages 377-390

About this book

Introduction

This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations.

Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier–Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.

Keywords

Navier–Stokes equations Navier-Stokes equations pullback attractors trajectory attractors classical hydrodynamics 2D Navier-Stokes equations dynamic motion of incompressible fluids mathematical physics

Authors and affiliations

  • Grzegorz Łukaszewicz
    • 1
  • Piotr Kalita
    • 2
  1. 1.Mathematics, Informatics and MechanicsUniversity of WarsawWarszawaPoland
  2. 2.Faculty of Mathematics and Computer SciJagiellonian University in KrakowKrakówPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-27760-8
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-27758-5
  • Online ISBN 978-3-319-27760-8
  • Series Print ISSN 1571-8689
  • Series Online ISSN 1876-9896
  • About this book