Literature cited
V. Arnold, “Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits,”Ann. Inst. Fourier,16, No. 1, 319–361 (1966).
D. J. Ebin and J. Marsden, “Diffeomorphism groups and the motion of incompressible fluid,” In:Transactions in Mathematics,17, No. 5, 142–167, No. 6, 111–146 (1973).
E. Nelson,Dynamical Theories of Brownian Motion, Princeton University Press, Princeton (1967).
E. Nelson,Quantum fluctuations, Princeton University Press, Princeton (1985).
Yu. E. Gliklikh, “Lagrange approach to the hydrodynamics of viscous incompressible fluid,”Uspekhi Mat. Nauk,45, No. 6, 127–128 (1990).
Yu. L. Daletskiiand Ya. I. Belopol'skaya,Stochastic Equations and Differential Geometry [in Russian], Vyshcha Shkola, Kiev (1989).
Yu. E. Gliklich,Calculus on Riemann Manifolds and Problems of Mathematical Physics, Voronezh State University, Voronezh (1989).
H. I. Eliasson, “Geometry of manifolds of maps,”J. Diff. Geometry,1, No. 2, 169–194 (1967).
G. T. Dankel, “Mechanics on manifolds and incorporation of spin into Nelson's stochastic mechanics,”Archive for Rational Mechanics and Analysis,37, 192–222 (1970).
S. Lang,Introduction to Differentiable Manifold [Russian translation], Mir, Moscow(1967).
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Translated from Matematicheskie Zametki, Vol. 55, No. 4, pp. 15–24, April, 1994.
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Gliklikh, Y.E. New version of the Lagrange approach to the dynamics of a viscous incompressible fluid. Math Notes 55, 344–350 (1994). https://doi.org/10.1007/BF02112472
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DOI: https://doi.org/10.1007/BF02112472