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  • © 2012

Compressible Navier-Stokes Equations

Theory and Shape Optimization

Birkhäuser
  • First monograph on the mathematical theory of shape optimization for compressible Navier-Stokes equations
  • Clear explanation of the state-of-the-art developments in a mathematical language that will attract mathematicians to open questions in this important field
  • New concepts and results are presented
  • Includes supplementary material: sn.pub/extras

Part of the book series: Monografie Matematyczne (MONOGRAFIE, volume 73)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xvi
  2. Preliminaries

    • Pavel Plotnikov, Jan Sokołowski
    Pages 1-44
  3. Physical background

    • Pavel Plotnikov, Jan Sokołowski
    Pages 45-55
  4. Problem formulation

    • Pavel Plotnikov, Jan Sokołowski
    Pages 57-61
  5. Basic statements

    • Pavel Plotnikov, Jan Sokołowski
    Pages 63-97
  6. Nonstationary case. Existence theory

    • Pavel Plotnikov, Jan Sokołowski
    Pages 99-166
  7. Pressure estimate

    • Pavel Plotnikov, Jan Sokołowski
    Pages 167-173
  8. Kinetic theory. Fast density oscillations

    • Pavel Plotnikov, Jan Sokołowski
    Pages 175-224
  9. Domain convergence

    • Pavel Plotnikov, Jan Sokołowski
    Pages 225-248
  10. Flow around an obstacle. Domain dependence

    • Pavel Plotnikov, Jan Sokołowski
    Pages 249-280
  11. Sensitivity analysis. Shape gradient of the drag functional

    • Pavel Plotnikov, Jan Sokołowski
    Pages 299-376
  12. Boundary value problems for transport equations

    • Pavel Plotnikov, Jan Sokołowski
    Pages 377-406
  13. Appendix

    • Pavel Plotnikov, Jan Sokołowski
    Pages 407-440
  14. Back Matter

    Pages 441-457

About this book

The book presents the modern state of the art in the mathematical theory of compressible Navier-Stokes equations, with particular emphasis on the applications to aerodynamics. The topics covered include: modeling of compressible viscous flows; modern mathematical theory of nonhomogeneous boundary value problems for viscous gas dynamics equations; applications to optimal shape design in aerodynamics; kinetic theory for equations with oscillating data; new approach to the boundary value problems for transport equations. The monograph offers a comprehensive and self-contained introduction to recent mathematical tools designed to handle the problems arising in the theory.

Authors and Affiliations

  • , Siberian Branch of RAS, Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia

    Pavel Plotnikov

  • , Institut Elie Cartan, Université Henri Poincaré Nancy 1, Vandœuvre-Lès-Nancy, France

    Jan Sokołowski

Bibliographic Information

  • Book Title: Compressible Navier-Stokes Equations

  • Book Subtitle: Theory and Shape Optimization

  • Authors: Pavel Plotnikov, Jan Sokołowski

  • Series Title: Monografie Matematyczne

  • DOI: https://doi.org/10.1007/978-3-0348-0367-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Basel 2012

  • Hardcover ISBN: 978-3-0348-0366-3Published: 04 August 2012

  • Softcover ISBN: 978-3-0348-0765-4Published: 20 September 2014

  • eBook ISBN: 978-3-0348-0367-0Published: 04 August 2012

  • Series ISSN: 0077-0507

  • Series E-ISSN: 2297-0274

  • Edition Number: 1

  • Number of Pages: XVI, 464

  • Topics: Partial Differential Equations, Mathematical Physics

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access