Mathematical Problems of Statistical Hydromechanics
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.
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analytic asymptotic Banach space bilinear operator Borel measure boundary values bounded domain Cauchy problem Chapter Clearly compact consider constructed continuous continuously embedded Corollary deduce defined Denote dense set depend derive distribution embedding estimate exists family of measures finite follows formula Fourier coefficients Fubini theorem functional spaces functional-analytic Galyerkin approximations Hence Hilbert space holds homogeneous measure homogeneous statistical Hopf equation Hull i(du implies individual solutions inequality initial measure initial value Kolmogorov equation Lemma let us prove Let us show linear mapping Mk(t moments Navier-Stokes equations norm obtain operator probability measure probability space problem 1.1 proof of Theorem Proposition random function REMARK satisfies scalar product similarly small Reynolds numbers solution u(t space-time statistical solution spatial statistical solution symmetric taking the limit tensor Theorem 1.1 unique solvability vector Wiener process zero