Translations of Mathematical Monographs 1995; 197 pp; hardcover Volume: 144 ISBN10: 0821802852 ISBN13: 9780821802854 List Price: US$96 Member Price: US$76.80 Order Code: MMONO/144
 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 NavierStokes equations for flows of a viscous fluid, and Reynolds equations for the mean velocity field, pressure, and pair onepoint 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 twodimensional flows
 A twodimensional passing flow problem for stationary Euler equations
 The dissipative top and the NavierStokes equations
 Specific features of turbulence models
 Appendix. Formal constructions connected with Euler equations
 References
