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Compressible Navier-Stokes Equations

Theory and Shape Optimization

  • Book
  • © 2012

Overview

Authors:
  1. Pavel Plotnikov

    1. , Siberian Branch of RAS, Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia

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  2. Jan Sokołowski

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

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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
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  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. Existence theory in nonsmooth domains. Shape optimization, continuity of the work functional

    • Pavel Plotnikov, Jan Sokołowski
    Pages 281-298

  12. Sensitivity analysis. Shape gradient of the drag functional

    • Pavel Plotnikov, Jan Sokołowski
    Pages 299-376

  13. Boundary value problems for transport equations

    • Pavel Plotnikov, Jan Sokołowski
    Pages 377-406

  14. Appendix

    • Pavel Plotnikov, Jan Sokołowski
    Pages 407-440

  15. Back Matter

    Pages 441-457
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Keywords

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

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