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Asymptotic Stability of Steady Compressible Fluids

  • Book
  • © 2011

Overview

Authors:
  1. Mariarosaria Padula

    1. Faculty of Engineering, Department of Mathematics, University of Ferrara, Ferrara, Italy

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  • 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.
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Topics in Fluid Mechanics

    • Mariarosaria Padula
    Pages 1-52

  3. Topics in Stability

    • Mariarosaria Padula
    Pages 53-86

  4. Barotropic Fluids with Rigid Boundary

    • Mariarosaria Padula
    Pages 87-132

  5. Isothermal Fluids with Free Boundaries

    • Mariarosaria Padula
    Pages 133-195

  6. Polytropic Fluids with Rigid Boundary

    • Mariarosaria Padula
    Pages 197-221

  7. Back Matter

    Pages 223-235
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Keywords

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)

Authors and Affiliations

  • Faculty of Engineering, Department of Mathematics, University of Ferrara, Ferrara, Italy

    Mariarosaria Padula

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