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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


Full text: PDF file (3859 kB)
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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
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    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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. D. A. Khrychev, “On the solubility of a non-linear hyperbolic equation with white noise”, Russian Math. Surveys, 36:3 (1981), 254–255  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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  mathnet  crossref  mathscinet  zmath
    6. I. V. Skrypnik, “Averaging of quasilinear elliptic problems in perforated domains”, Russian Math. Surveys, 40:4 (1985), 217–218  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Andro MikeliĆ, “Mathematical Problems of Statistical Hydromechanics (M. J. Vishik and A. V. Fursikov)”, SIAM Rev, 31:4 (1989), 704  crossref
    8. W. Kollmann, “The pdf approach to turbulent flow”, Theoret Comput Fluid Dynamics, 1:5 (1990), 249  crossref  zmath  adsnasa
    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  crossref  mathscinet  zmath  isi
    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  crossref
    11. N. G. Dokuchaev, “Boundary Value Problems for Functionals of Ito^ Processes”, Theory Probab Appl, 36:3 (1991), 459  mathnet  crossref  mathscinet  zmath  isi
    12. N. Elezović, A. Mikelić, “On the stochastic Cahn-Hilliard equation”, Nonlinear Analysis: Theory, Methods & Applications, 16:12 (1991), 1169  crossref
    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  crossref
    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  crossref
    15. V. I. Gishlarkaev, “Existence of statistical solutions of a stochastic Karman system in a bounded region”, Math. Notes, 58:1 (1995), 692–702  mathnet  crossref  mathscinet  zmath  isi
    16. Björn Schmalfuss, “Qualitative properties for the stochastic Navier–Stokes equation”, Nonlinear Analysis: Theory, Methods & Applications, 28:9 (1997), 1545  crossref
    17. A. R. Shirikyan, “Analyticity of solutions for randomly forced two-dimensional Navier–Stokes equations”, Russian Math. Surveys, 57:4 (2002), 785–799  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. Armen Shirikyan, “Qualitative properties of stationary measures for three-dimensional Navier–Stokes equations”, Journal of Functional Analysis, 249:2 (2007), 284  crossref
    19. Albeverio, S, “Some methods of infinite dimensional analysis in hydrodynamics: An introduction”, Spde in Hydrodynamic: Recent Progress and Prospects, 1942 (2008), 1  crossref  mathscinet  isi  elib
    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  crossref  elib
    21. Igor Chueshov, Annie Millet, “Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations”, Appl Math Opt, 2009  crossref  isi
    22. Sango M., “Density Dependent Stochastic Navier–Stokes Equations With Non-Lipschitz Random Forcing”, Reviews in Mathematical Physics, 22:6 (2010), 669–697  crossref  isi  elib
    23. Sango M., “Magnetohydrodynamic turbulent flows: Existence results”, Physica D-Nonlinear Phenomena, 239:12 (2010), 912–923  crossref  isi
    24. Igor Chueshov, Annie Millet, “Stochastic Two-Dimensional Hydrodynamical Systems: Wong-Zakai Approximation and Support Theorem”, Stochastic Analysis and Applications, 29:4 (2011), 570  crossref
    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  crossref
    26. D. A. Khrychev, “On large deviations for ensembles of distributions”, Sb. Math., 204:11 (2013), 1671–1690  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    27. Buckmaster T. Vicol V., “Convex Integration and Phenomenologies in Turbulence”, EMS Surv. Math. Sci., 6:1-2 (2019), 173–263  crossref  isi
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