Asymptotic Stability of Steady Compressible Fluids

  • Mariarosaria┬áPadula

Part of the Lecture Notes in Mathematics book series (LNM, volume 2024)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Mariarosaria Padula
    Pages 1-52
  3. Mariarosaria Padula
    Pages 53-86
  4. Mariarosaria Padula
    Pages 87-132
  5. Mariarosaria Padula
    Pages 133-195
  6. Mariarosaria Padula
    Pages 197-221
  7. Back Matter
    Pages 223-235

About this book

Introduction

This volume introduces a systematic approach to the solution of some mathematical problems that arise in the study of the hyperbolic-parabolic systems of equations that govern the motions of thermodynamic fluids. It is intended for a wide audience of theoretical and applied mathematicians with an interest in compressible flow, capillarity theory, and control theory.
The focus is particularly on recent results concerning nonlinear asymptotic stability, which are independent of assumptions about the smallness of the initial data. Of particular interest is the loss of control that sometimes results when steady flows of compressible fluids are upset by large disturbances. The main ideas are illustrated in the context of three different physical problems:
(i) A barotropic viscous gas in a fixed domain with compact boundary. The domain may be either an exterior domain or a bounded domain, and the boundary may be either impermeable or porous.
(ii) An isothermal viscous gas in a domain with free boundaries.
(iii) A heat-conducting, viscous polytropic gas.

Keywords

35-XX, 76-XX Compressible fluids: barotropic, polytropic Direct Lyapunov stability method Free boundary problem Free work equation Uniqueness of steady flows

Authors and affiliations

  • Mariarosaria┬áPadula
    • 1
  1. 1.Faculty of Engineering, Department of MathematicsUniversity of FerraraFerraraItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-21137-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-21136-2
  • Online ISBN 978-3-642-21137-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book