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This book presents applications of group analysis of differential equations to various models used in hydrodynamics. It contains many new examples of exact solutions to the boundary value problems for the Euler and Navier-Stokes equations. These solutions describe vortex structures in an inviscid fluid, Marangoni boundary layers, thermal gravity convection and other interesting effects. Moreover, the book provides a new method for finding solutions of nonlinear partial differential equations, which is illustrated by a number of examples, including equations for flows of a compressible ideal fluid in two and three dimensions. The work is reasonably self-contained and supplemented by examples of direct physical importance.
Audience: This volume will be of interest to postgraduate students and researchers whose work involves partial differential equations, Lie groups, the mathematics of fluids, mathematical physics or fluid mechanics.
|Foreword to the English Translation|
|Ch. 1||Group-Theoretic Classification of the Equations of Motion of a Homogeneous or Inhomogeneous Inviscid Fluid in the Presence of Planar and Rotational Symmetry|
|Ch. 2||Exact Solutions to the Nonstationary Euler Equations in the Presence of Planar and Rotational Symmetry|
|Ch. 3||Nonlinear Diffusion Equations and Invariant Manifolds|
|Ch. 4||The Method of Defining Equations|
|Ch. 5||Stationary Vortex Structures in an Ideal Fluid|
|Ch. 6||Group-Theoretic Properties of the Equations of Motion for a Viscous Heat Conducting Liquid|
|Ch. 7||Exact Solutions to the Equations of Dynamics for a Viscous Liquid|