**Translations of Mathematical Monographs**

1995;
197 pp;
Hardcover

MSC: Primary 76;
Secondary 35

**Print ISBN: 978-0-8218-0285-4
Product Code: MMONO/144**

List Price: $102.00

AMS Member Price: $81.60

MAA Member Price: $91.80

**Electronic ISBN: 978-1-4704-4561-4
Product Code: MMONO/144.E**

List Price: $96.00

AMS Member Price: $76.80

MAA Member Price: $86.40

# Nontraditional Methods in Mathematical Hydrodynamics

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*O. V. Troshkin*

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 & Endorsements

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

# Table of Contents

## Nontraditional Methods in Mathematical Hydrodynamics

- Cover Cover11
- Recent titles in series (continued in back) i2
- Title page v6
- Contents vii8
- Introduction 110
- Chapter I. Stationary flows of an ideal fluid on the plane 1120
- Chapter II. Topology of two-dimensional flows 2332
- Chapter III. A two-dimensional passing flow problem for stationary Euler equations 5362
- Chapter IV. The dissipative top and the Navier-Stokes equations 8998
- Chapter V. Specific features of turbulence models 133142
- Appendix. Formal constructions connected with Euler equations 163172
- References 191200
- Copy/Reprint page 199208
- Back Cover Back Cover1209