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 Uspekhi Mat. Nauk, 1979, Volume 34, Issue 5(209), Pages 135–210 (Mi umn4122)

This article is cited in 27 scientific papers (total in 27 papers)

Some mathematical problems of statistical hydromechanics

M. I. Vishik, A. I. Komech, A. V. Fursikov

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English version:
Russian Mathematical Surveys, 1979, 34:5, 149–234

Bibliographic databases:

UDC: 517.946
MSC: 76D06, 76D05, 37L65, 60G10, 76D03, 76Mxx
Received: 10.04.1979

Citation: M. I. Vishik, A. I. Komech, A. V. Fursikov, “Some mathematical problems of statistical hydromechanics”, Uspekhi Mat. Nauk, 34:5(209) (1979), 135–210; Russian Math. Surveys, 34:5 (1979), 149–234

Citation in format AMSBIB
\Bibitem{VisKomFur79} \by M.~I.~Vishik, A.~I.~Komech, A.~V.~Fursikov \paper Some mathematical problems of~statistical hydromechanics \jour Uspekhi Mat. Nauk \yr 1979 \vol 34 \issue 5(209) \pages 135--210 \mathnet{http://mi.mathnet.ru/umn4122} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=562801} \zmath{https://zbmath.org/?q=an:0495.76036|0503.76045} \transl \jour Russian Math. Surveys \yr 1979 \vol 34 \issue 5 \pages 149--234 \crossref{https://doi.org/10.1070/RM1979v034n05ABEH003906} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. D. A. Khrychev, “On a certain stochastic quasilinear hyperbolic equation”, Math. USSR-Sb., 44:3 (1983), 363–388
2. T. V. Girya, “Stabilization of statistical solutions of a non-linear parabolic equation with white noise”, Russian Math. Surveys, 36:2 (1981), 171–172
3. M. I. Vishik, A. I. Komech, “Weak solutions of the inverse Kolmogorov equation corresponding to the stochastic Navier–Stokes system”, Russian Math. Surveys, 36:3 (1981), 268–269
4. D. A. Khrychev, “On the solubility of a non-linear hyperbolic equation with white noise”, Russian Math. Surveys, 36:3 (1981), 254–255
5. I. D. Chueshov, “The existence of statistical solutions of the stochastic system of von Kármán equations in a bounded domain”, Math. USSR-Sb., 50:2 (1985), 279–298
6. I. V. Skrypnik, “Averaging of quasilinear elliptic problems in perforated domains”, Russian Math. Surveys, 40:4 (1985), 217–218
7. Andro MikeliĆ, “Mathematical Problems of Statistical Hydromechanics (M. J. Vishik and A. V. Fursikov)”, SIAM Rev, 31:4 (1989), 704
8. W. Kollmann, “The pdf approach to turbulent flow”, Theoret Comput Fluid Dynamics, 1:5 (1990), 249
9. Sergio Albeverio, Ana-Bela Cruzeiro, “Global flows with invariant (Gibbs) measures for Euler and Navier–Stokes two dimensional fluids”, Comm Math Phys, 129:3 (1990), 431
10. Atsushi Inoue, “On Hopf type functional derivative equations for □u + cu + bu2 + au3 = 0 on . I. Existence of solutions”, Journal of Mathematical Analysis and Applications, 152:1 (1990), 61
11. N. G. Dokuchaev, “Boundary Value Problems for Functionals of Ito^ Processes”, Theory Probab Appl, 36:3 (1991), 459
12. N. Elezović, A. Mikelić, “On the stochastic Cahn-Hilliard equation”, Nonlinear Analysis: Theory, Methods & Applications, 16:12 (1991), 1169
13. Dongho Chae, “The vanishing viscosity limit of statistical solutions of the Navier–Stokes equations. I. 2-D periodic case”, Journal of Mathematical Analysis and Applications, 155:2 (1991), 437
14. Dongho Chae, “The vanishing viscosity limit of statistical solutions of the Navier–Stokes equations. II. The general case”, Journal of Mathematical Analysis and Applications, 155:2 (1991), 460
15. V. I. Gishlarkaev, “Existence of statistical solutions of a stochastic Karman system in a bounded region”, Math. Notes, 58:1 (1995), 692–702
16. Björn Schmalfuss, “Qualitative properties for the stochastic Navier–Stokes equation”, Nonlinear Analysis: Theory, Methods & Applications, 28:9 (1997), 1545
17. A. R. Shirikyan, “Analyticity of solutions for randomly forced two-dimensional Navier–Stokes equations”, Russian Math. Surveys, 57:4 (2002), 785–799
18. Armen Shirikyan, “Qualitative properties of stationary measures for three-dimensional Navier–Stokes equations”, Journal of Functional Analysis, 249:2 (2007), 284
19. Albeverio, S, “Some methods of infinite dimensional analysis in hydrodynamics: An introduction”, Spde in Hydrodynamic: Recent Progress and Prospects, 1942 (2008), 1
20. I CHUESHOV, S KUKSIN, “Stochastic 3D Navier–Stokes equations in a thin domain and its α -approximation”, Physica D: Nonlinear Phenomena, 237:10-12 (2008), 1352
21. Igor Chueshov, Annie Millet, “Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations”, Appl Math Opt, 2009
22. Sango M., “Density Dependent Stochastic Navier–Stokes Equations With Non-Lipschitz Random Forcing”, Reviews in Mathematical Physics, 22:6 (2010), 669–697
23. Sango M., “Magnetohydrodynamic turbulent flows: Existence results”, Physica D-Nonlinear Phenomena, 239:12 (2010), 912–923
24. Igor Chueshov, Annie Millet, “Stochastic Two-Dimensional Hydrodynamical Systems: Wong-Zakai Approximation and Support Theorem”, Stochastic Analysis and Applications, 29:4 (2011), 570
25. Gabriel Deugoue, Mamadou Sango, “Weak solutions to stochastic 3D Navier–Stokes-α model of turbulence: α-Asymptotic behavior”, Journal of Mathematical Analysis and Applications, 384:1 (2011), 49
26. D. A. Khrychev, “On large deviations for ensembles of distributions”, Sb. Math., 204:11 (2013), 1671–1690
27. Buckmaster T. Vicol V., “Convex Integration and Phenomenologies in Turbulence”, EMS Surv. Math. Sci., 6:1-2 (2019), 173–263
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