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Nontraditional Methods in Mathematical Hydrodynamics
O. V. Troshkin, Moscow Technical University, Russia
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Translations of Mathematical Monographs
1995; 197 pp; hardcover
Volume: 144
ISBN-10: 0-8218-0285-2
ISBN-13: 978-0-8218-0285-4
List Price: US$91
Member Price: US$72.80
Order Code: MMONO/144
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This book discusses a number of qualitative features of mathematical models of incompressible fluids. Three basic systems of hydrodynamical equations are considered: the system of stationary Euler equations for flows of an ideal (nonviscous) fluid, stationary Navier-Stokes equations for flows of a viscous fluid, and Reynolds equations for the mean velocity field, pressure, and pair one-point velocity correlations of turbulent flows. The analysis concerns algebraic or geometric properties of vector fields generated by these equations, such as the general arrangement of streamlines, the character and distribution of singular points, conditions for their absence or appearance, and so on. Troshkin carries out a systematic application of the analysis to investigate conditions for unique solvability of a number of problems for these quasilinear systems. Containing many examples of particular phenomena illustrating the general ideas covered, this book will be of interest to researchers and graduate students working in mathematical physics and hydrodynamics.

Readership

Researchers and graduate students working in mathematical physics and hydrodynamics.

Reviews

"The book overall treats a number of very special problems ... from an interesting perspective."

-- Mathematical Reviews

"Can be used by researchers and graduate students working in mathematical physics and hydrodynamics."

-- Zentralblatt MATH

Table of Contents

  • Introduction
  • Stationary flows of an ideal fluid on the plane
  • Topology of two-dimensional flows
  • A two-dimensional passing flow problem for stationary Euler equations
  • The dissipative top and the Navier-Stokes equations
  • Specific features of turbulence models
  • Appendix. Formal constructions connected with Euler equations
  • References
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