Abstract
In this paper, we investigate the connection between crystallographic groups and homogeneous statistical solutions of Navier-Stokes equations. Several results of Foias and Temam are extended. Fluid flows invariant under crystallographic groups are studied. This idea may be of interest to the understanding of bifurcation and turbulence.
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References
G. K. Batchelor,The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1953).
C. Foias, Statistical Study of the Navier-Stokes equations, I,Rend. Semin. Mat. Univ. Padova 48:219–348, (1972); II,Rend. Seminan. Mat. Univ. Padova 49:9–123, (1973).
C. Foias, Ergodic problems in functional spaces related to Navier-Stokes equations,Proc. Int. Conf. Funct. Anal., Tokyo (1969), 290–304.
C. Foias and R. Temam, Homogeneous statistical solutions of Navier-Stokes equations, University of Paris-Sud, Orsay, 1980.
I. M. Gel'fand, M. I. Graev, and I. I. Pyatetskii-Shapiro,Representation theory and automorphic functions (Saunders, Philadelphia, 1969).
E. Hopf, Statistical hydrodynamics and functional calculus,Rat. Mech. Anal. 16:87–123 (1948).
K. Kirchgassner and H. Kielhöfer, Stability and bifurcation in fluid mechanics,Rocky Mount. J. Math. 3:275–318 (1973).
R. Temam,Navier-Stokes Equations (North-Holland, Amsterdam, 1979).
M. I. Vishik and A. V. Foursikov, Solutions statistiques homogenes des systemes differentiels paraboliques et du systeme de Navier-Stokes,Anali Scuola Norm. Sup. Pisa, Serie IV, Vol. IV, 3, 531–576 (1977).
M. I. Vishik and A. V. Foursikov, Translationally homogeneous statistical solutions and individual solutions with infinite energy of a system of Navier-Stokes equations,Siber. Math. J. 19(5):710–729 (1978).
J. Wolf,Spaces of Constant Curvature (McGraw-Hill, New York, 1967).
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Chen, S.S. Crystallographic groups and homogeneous statistical solutions of navier-stokes equations. J Stat Phys 29, 579–589 (1982). https://doi.org/10.1007/BF01342188
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DOI: https://doi.org/10.1007/BF01342188