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Translationally homogeneous statistical solutions and individual solutions with infinite energy of a system of Navier-Stokes equations. (English) Zbl 0412.35078

MSC:
35Q30 Navier-Stokes equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76D05 Navier-Stokes equations for incompressible viscous fluids
76F05 Isotropic turbulence; homogeneous turbulence
35A35 Theoretical approximation in context of PDEs
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References:
[1] S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, Amer. Math. Soc. (1969). · Zbl 0233.42013
[2] M. I. Vishik and A. V. Fursikov, ?Homogeneous statistical solutions of the Navier-Stokes system,? Usp. Mat. Nauk,32, No. 5, 179-180 (1977). · Zbl 0363.35033
[3] M. I. Vishik and A. V. Fursikov, ?Homogeneous statistical solutions of parabolic systems of differential equations and of the Navier-Stokes system,? Ann. Scuola Norm. Sup. Pisa, Ser. IV,4, No. 3, 531-576 (1977).
[4] O. A. Ladyzhenskaya, Mathematical Theory of Viscous Incompressible Flow, Gordan and Breach (1969). · Zbl 0184.52603
[5] K. Yosida, Functional Analysis, Springer-Verlag, New York (1971). · Zbl 0217.16001
[6] I. I. Gikhman and A. V. Skorokhod, The Theory of Stochastic Processes, Springer-Verlag (1975). · Zbl 0348.60042
[7] G. E. Shilov, Mathematical Analysis, A Special Course, Pergamon (1965). · Zbl 0137.26203
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