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  • © 2015

Mathematical Models of Viscous Friction

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2135)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xiv
  2. Gas of Point Particles

    • Paolo Buttà, Guido Cavallaro, Carlo Marchioro
    Pages 1-41
  3. Vlasov Approximation

    • Paolo Buttà, Guido Cavallaro, Carlo Marchioro
    Pages 43-61
  4. Motion of a Body Immersed in a Vlasov System

    • Paolo Buttà, Guido Cavallaro, Carlo Marchioro
    Pages 63-100
  5. Motion of a Body Immersed in a Stokes Fluid

    • Paolo Buttà, Guido Cavallaro, Carlo Marchioro
    Pages 101-116
  6. Back Matter

    Pages 117-136

About this book

In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion.

Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some aspects of the proof if it is prohibitively technical.

This book is principally addressed to researchers or PhD students who are interested in this or related fields of mathematical physics.

Keywords

  • 70F40;78A35;34G20;70F45;82C05;82C40;76D07.
  • Body/medium interaction
  • Hamiltonian systems
  • Memory effects
  • Ohm's law
  • Viscous friction
  • ordinary differential equations
  • fluid- and aerodynamics
  • partial differential equations

Reviews

“This book presents some results from the mathematical theory of viscous friction that describes the motion of a body immersed in an infinitely extended medium and subjected to the action of an external force. … Each chapter ends with its own list of references relevant to the topics covered in the respective chapter. These are helpful features that increase the accessibility of the book. The intended audience would be graduate students and other researchers in applied mathematics or mathematical physics.” (Lucy J. Campbell, Mathematical Reviews, October, 2015)

Authors and Affiliations

  • Dept. of Mathematics, Sapienza Università di Roma, Roma, Italy

    Paolo Buttà, Guido Cavallaro, Carlo Marchioro

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions