Mathematical Problems of Statistical Hydromechanics

✍ Scribed by M. J. Vishik, A. V. Fursikov (auth.)

• Publisher: Springer Netherlands
• Year: 1988
• Tongue: English
• Leaves: 583
• Series: Mathematics and Its Applications (Soviet Series) 9
• Edition: 1
• Category: Library

✦ Synopsis

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The ScandiJI of Father 'The Hermit Clad in Crane Feathers' in R. Brow" 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

✦ Table of Contents

Front Matter....Pages i-ix
Introduction....Pages 1-8
Functional-Analytic Expansions of Solutions of Evolution Equations....Pages 9-53
Elements of Measure Theory....Pages 54-68
Moment Theory for Small Reynolds Numbers....Pages 69-117
Space-Time Statistical Solutions of the Navier-Stokes Equations for Arbitrary Reynolds Numbers....Pages 118-146
The Hopf Equation....Pages 147-172
Moment Theory for Arbitrary Reynolds Numbers....Pages 173-203
Homogeneous Space-Time Statistical Solutions of Navier-Stokes Equations....Pages 204-258
Individual Solutions with Unbounded Energy for Navier-Stokes Equations and Other Problems....Pages 259-291
Analytic First Integrals and Asymptotic Behaviour as t → ∞ of Fourier Coefficients of Solutions of Two-Dimensional Navier-Stokes Equations....Pages 292-334
Navier-Stokes System with White Noise in a Bounded Domain....Pages 335-375
The Direct and Inverse Kolmogorov Equations Corresponding to a Stochastic Navier-Stokes System....Pages 376-430
Homogeneous in x Solutions of the Stochastic Navier-Stokes System with White Noise....Pages 431-473
Back Matter....Pages 474-576

✦ Subjects

Statistics, general;Mechanics;Analysis