Nontraditional methods in mathematical hydrodynamics
著者
書誌事項
Nontraditional methods in mathematical hydrodynamics
（Translations of mathematical monographs, v. 144）
American Mathematical Society, c1995
- タイトル別名
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Нетрадиционные задачи математической гидродинамики
Netradit︠s︡ionnye zadachi matematicheskoĭ gidrodinamiki
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注記
Translation of: Netradit︠s︡ionnye zadachi matematicheskoĭ gidrodinamiki
Includes bibliographical references (p. 191-197)
内容説明・目次
内容説明
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.
目次
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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