Abstract
The variables for the complete description of the statistical properties of turbulence in incompressible Newtonian fluids and the associated equations governing them are set up and their fundamental properties, such as mathematical type, linearity/nonlinearity, solvability, etc., are discussed in the present section.
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References
Cartier, P., DeWitt-Morette, C.: A new perspective on functional integration. J. Math. Phys. 36, 2137–2340 (1995)
DeWitt-Morette, C., Cartier, P., Folacci, A.: Functional Integration. Plenum Press, New York, London (1997)
Cartier, P., DeWitt-Morette, C.: Functional Integration: Action and Symmetries. Cambridge University Press, Cambridge U.K (2006)
Simon, B.: Functional Integration and Quantum Physics. AMS Chelsea Publication, Providence, Rhode Island (2004)
Klauder, J.R.: A Modern Approach to Functional Integration. Birkhaeuser/Springer, New York (2010)
Vishik, M.J., Fursikov, A.V.: Mathematical Problems of Statistical Hydromechanics. Kluwer Academic Publication, Dordrecht (1988)
Dalecky, Y.L., Fomin, S.V.: Measures and Differential Equations in Infinite-Dimensional Space. Kluwer Academic Publication, Dordrecht (1991)
Shilov, G.E., Gurevich, B.L.: Integral, Measure and Derivative: A Unified Approach. Prentice Hall Inc., Englewood Cliffs (1966)
Bogachev, V.I.: Measure Theory, vol. 1. Springer, New York (2006)
Yamasaki, Y.: Measures on Infinite Dimensional Spaces. World Scientific, Singapure (1985)
Conway, J.: A Course in Functional Analysis. Springer, New York (1990)
Kreyszig, E.: Introductory Functional Analysis with Applications. Wiley, New York (1989)
Minlos, R.A.: Cylinder sets. In: Hazewinkel, M. (ed.) Encyclopdia of Mathematics. Springer, New York (2001)
Skorohod, A.V.: Integration in Hilbert Space. Springer, New York (1974)
Bogachev, V.I.: Gaussian Measures, Mathematical surveys and monographs, p. 62. American Mathematical Society (1998)
Sagaut, P., Cambron, C.: Homogeneous Turbulence Dynamics. Cambridge University Press, New York (2008)
Kuksin, S., Shirikyan, A.: Mathematics of Two-dimensional Turbulence, Cambridge Tracts in Mathematics, vol. 194. Cambridge University Press, U.K. (2012)
Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge, U.K. (2001)
Cameron, R.H., Martin, W.T.: Transformations of Wiener integrals under a general class of linear transformations. Trans. Am. Math. Soc. 58, 184–219 (1945)
Cameron, R.H., Martin, W.T.: Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations. Bull. Am. Math. Soc. 51, 73–90 (1945)
Hartmann, P.: Ordinary Differential Equations. SIAM, Philadelphia (2002)
Duffy, D.G.: Greenś Functions with Applications. Chapman & Hall/CRC, Boca Raton, Florida (2001)
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Kollmann, W. (2019). Probability Measure and Characteristic Functional. In: Navier-Stokes Turbulence. Springer, Cham. https://doi.org/10.1007/978-3-030-31869-7_6
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DOI: https://doi.org/10.1007/978-3-030-31869-7_6
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