Lecture Notes in Mathematics

Asymptotic Stability of Steady Compressible Fluids

Authors: Padula, Mariarosaria

  • It is the first book specifically devoted to nonlinear stability of compressible fluids.
  • A systematic approach is proposed.
  • It turns out of great utility to graduate students, since it is self--contained and only basic elements of functional analysis and PDE are required. Original techniques are introduced in the study of direct Lyapunov method, these techniques furnish, in particular new "a priori" estimates for the solutions.
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  • ISBN 978-3-642-21137-9
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Softcover $59.95
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  • ISBN 978-3-642-21136-2
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About this book

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.

Reviews

From the reviews:

“The subject of the book is the dynamic stability of steady flows of fluids. … The book considers many different boundary conditions with fixed and free boundaries. … the book is well written and of interest to everyone working on the questions of stability, in particular global stability of compressible viscous fluid flows. It also provides an extensive list of references about the subject matter.” (Gerhard O. Ströhmer, Mathematical Reviews, January, 2013)


Table of contents (1 chapters)

  • Isothermal Fluids with Free Boundaries

    Mariarosaria Padula

    Pages 133-195

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-21137-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-21136-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Asymptotic Stability of Steady Compressible Fluids
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2024
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-21137-9
DOI
10.1007/978-3-642-21137-9
Softcover ISBN
978-3-642-21136-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 235
Topics