Troshkin, O.V. Nontraditional methods in mathematical hydrodynamics (Translations of mathematical monographs, ISSN 0065-9282; v. 144)
Abstract. The main goal of the book is to present a number of features of mathematical models for incompressible fluids. Three basic systems of hydrodynamical equations are considered, namely, the system of stationary Euler equations for flows of 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, etc. The information provided by this analysis is Used for the investigation of the conditions for unique solvability of a number of problems for these quasilinear systems. The book contains a lot of examples of particular phenomena illustrating general ideas in the book. The book can be used by researchers and graduate students working in mathematical physics and hydrodynamics.