Generalization of the Millennium Prize problem to the Navier–Stokes (NS) equation for compressible medium

Sergey G. Chefranov,
Ph.D., Doctor of Phys. and Math. Sci.

Curriculum vitae


143036, Russia, Moscow region, Odintzovo district, Zvenigorod science station, A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Science, Novoshihovo, 4


office: +7 (495) 951-13-47
home: +7 (916) 947-63-58
fax: +7 (495) 953-21-58


Date and place of birth:

October 30, 1951, Leningrad, Russia


  • 1968–1974 Moscow Institute of Physics and Technics (in Dolgoprudni), Faculty of Molecular and Chemical Physics, M.Sc. Thesis: "Convective instability in fluid during heterogeneous catalytic chemical reaction" (Institute of Chemical Physics, Chernogolovka, Moscow region); Supervisor: Prof. Emil A. Shtessel
  • 1975–1979 USSR Academy of Science, Institute of Atmospheric Physics, Moscow. Ph.D. (specialization in geophysics), Thesis: "Statistical Stability and Predictability of Turbulent Flows", supervisor: Prof. Evgeny A. Novikov
  • 1992 Russian Academy of Science (RAS), Institute of Space Research (ISP), Moscow. Doctor of Physics and Mathematics (specialization in theoretical physics), Thesis: "Predictability and Structures of Vortex and Admixture Fields in Turbulent Medium", science consultant: Prof. Akiva M. Yaglom

Professional experience

  • Since 1974 Leading Scientist, A.M. Obukhov Institute of Atmospheric Physics (IAP), Russian Academy of Science (RAS), Moscow, Russia
  • 1998–2003 Leading Scientist, Institute of Theoretical and Experimental Biophysics (ITEB), Russian Academy of Science, Pushchino, Moscow region, Russia
  • Research interests

    • Theory of hydrodynamics and turbulence: (a) Exact solutions for the dynamics of vorticity; (b) Coherent structures; (c) Turbulent diffusion; (d) Predictability; (e) MGD–turbulence
    • Nonlinear Dynamical System (in Biology and Physics)
    • Bionics (engineering of the paragliding wings, which may use turbulence energy as in bird wings)
    • Theory of Electro-Magnetic Fields in Media (based on Abraham’s theory)
    • Quantum theory of gravity and cosmology


Member of scientific and professional associations

  • New York Academy of Science - active member from January 1995
  • European Mechanics Society - active member from June 2011

Referee for the following journals

  • Physics Letters A
  • Journal of High Energy Physics, Gravitation and Cosmology

List of publication

  1. E.A. Novikov, S.G. Chefranov, Nonlinear evolution of disturbances in turbulent flows and predictability problem, IRAS, AOP, 13,№6, 611-619, 1977
  2. E.A. Novikov, S.G. Chefranov, Statistical stability and evolution of disturbances for stationary regimes of turbulent flows, Preprint IAP RAS, Moscow, 1978
  3. S.G. Chefranov, Predictability of vertical non-homogenous atmospheric flows, IRAS, AOP, 14, №12, 1298-1302, 1978
  4. S.G. Chefranov, Spectral analysis of quasi-two-dimensional atmospheric turbulence and the problem of predictability, Preprint IAP AS USSR, Moscow, 1979.
  5. S.G. Chefranov, The influence of smoothness of forecasting fields on their predictability, IRAS, AOP, 16, №6, 690-693, 1980
  6. S.G. Chefranov, A.G. Chefranov, Parametric excitation of internal waves and convective instability in the layer of fluid which heated from above, IRAS, AOP, 19, №7, 741-749, 1983
  7. S.G. Chefranov, The modeling of global pollution transfer in atmosphere, IRAS, AOP, 21, №10, 1026-1035, 1985
  8. S.G. Chefranov, Relaxation of the modulus of the order parameters for T>Tc and the nonstationary proximity effects, Soviet J. Low Temp. Phys, 11, №5, 464-468, 1985
  9. S.G. Chefranov, The theory of large scale turbulent transport of chemical active pollutions, Izv. Vuzov Radiophizika, 28, №12, 1516-1523, 1985
  10. S.G. Chefranov, Vortex diffusion of passive pollution, IRAS, AOP, 23, №6, 659-661, 1987
  11. S.G. Chefranov, Kinetic transition of medium occupation type and the origin of dusty storms on Mars, IRAS, AOP, 23, №12, 1422-1428, 1987.
  12. S.G. Chefranov, Dynamics of point vortex dipoles and spontaneous singularities in three – dimensional turbulent flows, JETP, 93(7), 151-158, 1987.
  13. S.G. Chefranov, The theory of turbulent diffusion in the inertial sub-range, IRAS, AOP, 24, №5, 499-505, 1988
  14. S.G. Chefranov, Relative diffusion of passive admixture particles in a turbulent flow, IRAS, AOP, 24, №8, 800-808, 1988
  15. S.G. Chefranov, Spontaneous singularities in 3-D turbulence and the emission of sound during strong dynamical interaction between point vortex dipoles, JETP, 94(5), 112-115, 1988.
  16. S.G. Chefranov, Relative diffusion of the particles of passive pollution in the turbulent flow, IRAS, AOP, 24, №8, 800-808, 1988
  17. S.G. Chefranov, On Lagrangian statistical characteristics of turbulence and intermittency effects, IRAS, AOP, 25, №6, 502-598, 1989
  18. S.G. Chefranov, Diffusion of impurities in the field of intense vortex and the problem of Antarctic ozone depletion, Meteorology and Hydrology, №7, 31-38, 1989
  19. S.G. Chefranov, Regularization of self-energy of point vortex dipoles and the increase in total vorticity (enstrophy) during stretching of vortex lines, JETP, 95(2), 547-561, 1989.
  20. S.G. Chefranov, On the theory of turbulent viscosity, JETP, 96(7), 171-186, 1989.
  21. S.G. Chefranov, The spectral current of energy and enstrophy in barotropic atmospheric turbulence and the predictability of pollution fields in the presence of orographical disturbances, IRAS, AOP, 26, №8, 801-812, 1990
  22. S.G. Chefranov, Effective diffusion in finite stochastically inhomogeneous medium threshold raising of global dusty storms on Mars, IRAS, AOP, 27, №7, 58-66, 1991
  23. S.G. Chefranov, Exact statistically closure description of vortex turbulence and admixture in compressible medium, Sov. Phys. Dokl., 36 (4), 286-289, 1991.
  24. S.G. Chefranov, Dynamic of point vortex quadrupoles and elliptic vortexes on plane, JETP, 99, №4, 1149-1165, 1991
  25. S.G. Chefranov, Effective diffusion, localization and predictability of the dynamics of Lagrange particles of pollution in vortex fields above orographic non-uniformities, IRAS, AOP, 28, №8, 828-836, 1992
  26. S.G. Chefranov, Predictability and structures of the fields of vortex and pollution in the turbulent media. Abstract of dissertation of Doctor of Science (field- theoretical physics), Institute of Cosmic Research RAS, Moscow, 1992
  27. S.G. Chefranov, Effective diffusion, localization and predictability of dynamic of Lagrangian particles of admixture in vertical flows over a topography, IRAS, AOP, 28, №8, 828-836, 1992
  28. S.G. Chefranov, Turbulent diffusion in stable stratified atmosphere, IRAS, AOP, 29, №1, 19- 28, 1993
  29. S.G. Chefranov, Turbulent diffusion and intermittence, JETP, 108, 5(12), 2010-2020, 1995.
  30. X.A. Akmamedova, S.G. Chefranov, N.N. Pertzev,,About the possible mechanism of temperature disturbance during Iran earthquake in June 1990, Geomagnetism and Aeronome, 36, №2, 119-123, 1996.
  31. S.G. Chefranov, Intermittency and turbulent diffusion, “Dynamics Days”, 17th Ann. Inform. Workshop, Ecole Normal Superior De Lyon, July 10-13, 1996
  32. S.G. Chefranov, Long-range dust transfer inside boundary layer in the presence of wind shear and temperature inversion. Tech. Report Institute of Atmospheric Physics RAS, Prog. №35, 1996
  33. S.G. Chefranov, A.V. Gusev, I.S. Ilyin, Comparison of computations using ASIMD model with exact solutions of the problem of the diffusion of pollution in shifted flows, ЕМЕР, MSC-E, Tech. Report, 1998
  34. S.G. Chefranov, A.Yu. Abramichev, A.B. Tankanag, Hybrid Euler-Lagrange Model (HELM) of far pollution transport, EMEP, MSC-E, Tech. Report, 1998
  35. S.G. Chefranov, A.I. Nebozhin, A.I. Nevzorov, Biophysical aspects of diagnostics and correction of clinical states of cranium, Traditional methods of curing – main trends and perspectives of development. Ministry of Health, Russian Federation, Moscow, 1998
  36. S.G. Chefranov, On the possibility of realization of analogue of hydrodynamic effect of Thoms in the fundamental improving of anti-dropsical characteristics of hemo- and liqueur dynamics when using blood substitute of “Perftoran” type, Trasactions of Science Center of Biology Research, Peftoran-organic combinations in biology and medicine, 218-222, Pushchino, RAS, 1999
  37. S.G. Chefranov, On stochastization of intracellular calcium waves, ITEB RAS, Pushchino, 1999
  38. N.K. Chemeriz, S.G. Chefranov, Some physico-chemical mechanisms of low-intensive impact of electromagnetic radiation of mm-band on biological objects: laboratory modeling in liquid media with creation of vortex hydrodynamic structures of the thermals type, ITEB RAS, Puschino, 1999
  39. S.G. Chefranov, Centrifugal–dissipative instability and cyclonic–anticyclonic asymmetry of Rossby vortices, JETP Lett., 73, №6, 274-278, 2001.
  40. S.G. Chefranov, About scale-invariant-similarity criterion of swirling flows for tornado-like laboratory modeling, IRAS, AOP, 39, №6, p.685, 2003
  41. A.S. Chefranov, S.G. Chefranov, Extrema of the kinetic energy and its dissipative rate in the hydromechanics of swirling flows, Doklady Physics RAS, 393, №5, 624-628, 2003.
  42. S.G. Chefranov, A New Approach to the Theory of Cherenkov Radiation Based on Relativistic Generalization of the Landau Criterion, JETP, 99, 296-310, 2004.
  43. S.G. Chefranov, Helicity Generation in Uniform Helical Flows, JETP, 99, 987-997, 2004.
  44. S.G. Chefranov, Relativistic generalization of the Landau Criterion as a New Foundation of the Vavilov–Cherenkov radiation theory, Phys. Rev. Lett., 93, 254801, 2004
  45. S.G. Chefranov, The relativistic generalization of the Landau criterion. Proc of Int. Conf. MSS-04, Mode conversion, coherent structures and turbulence, Nov. 23-25, Russian Acad. of Science, Institute of Space Research (ISR RAS), Moscow, 2004, pp. 99-104
  46. V.N. Blazhko, S.G. Chefranov, On the possible linear dissipative-centrifugal instability mechanism of tropical cyclone (typhoon) early stage development, Proc. Int. Conf. MCC-04, ISR RAS, Moscow, 2004, pp. 238-242, 2004
  47. S.G. Chefranov, On the vortex and helicity generation in rotating systems with temperature in homogeneity, Proc. Int. Conf. MCC-04, ISR RAS, Moscow, 2004, 415-419
  48. S.G. Chefranov, Exact Solution of hydrodynamic equations and realization of swirling flows in cardio-vascular system. Proc. of Russian Academy of Science, Conf. on Program of Basic Research "Basic Research – for Medicine", Dec. 2-3, Moscow, 2004 4
  49. V.N. Blazhko, S.G. Chefranov, Dissipative-centrifugal instability of tropical disturbances and initial stage of development of tropical cyclones, IRAS, AOP, 41, №5, 593-601, 2005
  50. V.N. Blazhko, S.G. Chefranov, On auto-oscillations emerging when swirled flow pours, Izvestiya RAS, Mechanics of Fluid and Gas, №5, 99-106, 2005.
  51. S.G. Chefranov, G.V. Kovrov, Mathematical modeling of scaled similar macro-structured organization of sleep and integral characteristic of its effectiveness, Doklady RAS, 407, 706- 711, 2006
  52. S.G. Chefranov, Maximal volumetric spending of fluid and “golden” angle of the swirled flow in a pipe, Doklady RAS, 426, 328-331, 2009.
  53. S.G. Chefranov, E.A. Novikov, Hydrodynamic vacuum sources of dark matter self-generation in accelerated universe without Big Bang, JETP, 111, 731-741, 2010.
  54. I.I. Mokhov, S.G. Chefranov, A.G. Chefranov, Dynamics of δ-Singular Vortexes on a Rotating Sphere and Stability of Paired Action Centers of the Atmosphere, Doklady RAS, 433, Part 1, 948–953, 2010.
  55. S.G. Chefranov, E.A. Novikov, Hydrodynamic Vacuum Sources of Dark Matter SelfGeneration in Accelerated Universe without Big Bang, arXiv:1012.0241v1, 2010
  56. S.G. Chefranov, The Vavilov-Cherenkov radiation by relict photon gas, arXiv:1009.0594, 2010.
  57. I.I. Mokhov, S.G.Chefranov, A.G. Chefranov, Delta-singular vortex dynamics on a rotating sphere and stability of coupled atmospheric centers of action, arXiv:1009.0333, 2010.
  58. S.G. Chefranov, A.G. Chefranov, Linear Exponential Instability of the Hagen-Poiseuille Flow with Respect to Synchronous Bi-Periodic Disturbances, arXiv:1007.3586, 2010.
  59. S.G. Chefranov, A.G. Chefranov, Hagen-Poiseuille Flow Linear Stability Paradox Resolving and Viscous Dissipative Mechanism of the Turbulence Emergence, arXiv:1007.1097, 2010
  60. E.A. Novikov, S.G. Chefranov, A quiet cosmology and halo around visible universe, J. Cosmology, 16, 6884, 2011.
  61. S.G. Chefranov, E.A.Novikov, Halo Around Universe, Proc. PANic (Particles and Nuclear Intern. Conf.) – 11, Rutherford Centennial, MIT, Cambridge MA, July 24-29 2011
  62. S.G. Chefranov, A.G. Chefranov, A.S. Chefranov, Hydro-Mechanical Foundations for the Blood Swirling Vortex Flows in Cardiovascular System, Proc. of European Mechanics Society Colloquium 529 “Cardiovascular Fluid Dynamics: From theoretical aspects to diagnostic and therapeutic support “, Univ. of Cagliari, Cagliari, Italy, 27-29 June 201
  63. S.G. Chefranov, A.G. Chefranov, New Linear Theory of Hydrodynamic Instability of the Hagen–Poiseuille Flow,, 2011
  64. S.G. Chefranov, A.G. Chefranov, New linear theory of hydrodynamic instability of the Hagen-Poiseuille flow and the blood swirling flow formation, Cardiometry, ( No.1, 24-30, 2012.
  65. S.G. Chefranov, A.G. Chefranov, A.S. Chefranov,, The influence of the atmospheric pressure variations on the energetic effectiveness of the cardiovascular system function, Proc. Intern. Conf. “On the influence of Space weather on man: in the Space and on the Earth “, Institute of Space Research, RAS, Moscow, 2012
  66. S.G. Chefranov, Generalization of the Einstein- Plank- Richardson law for the photon energy in medium resolves Abraham-Minkowski dilemma in the electromagnetic field theory statement,, 2012
  67. S.G. Chefranov, The new microscopic Vavilov-Cherenkov radiation theory,, 2012
  68. S.G. Chefranov, New quantum theory of the Vavilov-Cherenkov radiation and its analogues,, 2012
  69. I.I. Mokhov, S.G. Chefranov, A.G. Chefranov, Interaction of the Global-Scale Atmospheric Vortices: Modeling Based on Hamiltonian system for Antipodal Vortices on Rotating Sphere,, 2012. 5
  70. S.G. Chefranov, On the possible mechanism of effecting of environmental factors on energy effectiveness of cardio-vascular system functioning, Cardiometry, ( No.2, 40-50, 2013.
  71. S.G. Chefranov, A.G. Chefranov, A.S. Chefranov, Hydromechanics foundations for blood swirling flow formation in the cardio- vascular system and the problem of the artificial heart creation, Cardiometry, (, No.3, 52-64, 2013.
  72. S.G. Chefranov, On condition of negativity of friction resistance for non-stationary model of blood flow and possible mechanism of affecting of environmental factors on energy effectiveness of cardio-vascular system functioning,, 2013
  73. S.G. Chefranov, A.G. Chefranov, V. Venugopal, Compton Effect in the Medium with NonUnity Refractive Index,, 2013
  74. S.G. Chefranov, A.G. Chefranov, Parametric excitation of internal gravity waves in ocean and atmosphere as precursors of strong earthquakes and tsunami,, 2013
  75. S.G. Chefranov, Linear Eckman friction in the mechanism of the cyclon-anticyclon vortex asymmetry and in a new theory of rotating superfluid,, 2014
  76. S.G. Chefranov, A.G.Chefranov, Collapse of Point Vortex Dipoles in a Bounded Fluid Layer and the Hydrodynamic Mechanism of Mutual Attraction of Like-Charged Micro-Particles in the Colloid or Dusty Plasma Systems,, 2014
  77. S.G. Chefranov, A.G. Chefranov, Solution to the paradox of the linear stability of the HagenPoiseuille flow and viscous dissipative mechanism of the emergence of turbulence in a boundary layer, JETP, 119, 331-340, 2014.
  78. S.G. Chefranov, A.G. Chefranov, The Hagen-Poiseuille Linear Flow Instability, Doklady RAS, 60, No.7, 327-332, 2015.
  79. S.G. Chefranov, A.G. Chefranov, Linear instability of the plane Couette and plane Poiseuille flows,, 2015
  80. S.G. Chefranov, Cyclon-anticyclone vortex asymmetry mechanism and linear Ekman friction, JETP, 122, 759-768, 2016.
  81. S.G. Chefranov, A.G. Chefranov, Linear instability of plane Couette and Poiseuille flows, JETP, 122, 920-931, 2016.
  82. S.G. Chefranov, Vavilov-Cherenkov radiation when cosmic rays pass through the relic photon gas and when fast charged particles traverse an optical laser beam, JETP, 123, 12-16, 2016.
  83. I.I. Mokhov, S.G. Chefranov, A.G. Chefranov, Interaction between global-scale atmospheric vortices: Modeling with Hamiltonian dynamic system of antipodal point vortices on a rotating sphere,, 2017
  84. S.G. Chefranov, Energy-Optimal Time-Dependent Regimes of Viscous Incompressible Fluid Flow, Fluid Dynamics, 52, No.2, 201-214, 2017.
  85. S.G. Chefranov, A.G. Chefranov, Dissipative soliton vortices and tropical cyclones, JETP, 125 (4), 714-717, 2017
  86. S.G. Chefranov, A.S. Chefranov, Exact Time-Dependent Solution to the Three-Dimensional Euler-Helmholtz and Riemann-Hopf Equations for Vortex Flow of a Compressible Medium and the Sixth Millennium Prize Problem,, [physics.gen-ph] 13 Jul 2017
  87. S.G. Chefranov, A.S. Chefranov, Exact time-dependent solution to the Euler-Helmholtz and Riemann-Hopf equations, Proc. Turbulent Mixing and Beyond, Sixth Int. Conf. Tenth Ann. Prog., 14-18 Aug A. Salam Int. Center for Theoretical Physics, Trieste, Italy, 2017
  88. S.G. Chefranov, A.S. Chefranov, The new analytical solution of the 3-D Navier-Stokes equation for compressible medium clarifies the Sixth Millennium Prize Problem, 311-341, Science, Technology, Society and International Nobel Movement, Proc. Int. Nobel CongressXI-th Int. Meeting-Conference for Nobel Prize Winners and nobelists, 24-28 Oct, Tambov, Russia, 2017
  89. S.G. Chefranov, A.G. Chefranov, Dissipative-centrifugal instability of the Burgers vortex core and cyclone-anticyclone vortex asymmetry, [physics.fludyn] 29 Oct 2017
  90. S.G. Chefranov, A.S. Chefranov, The exact solution to the vortex 3-D Euler equation for compressible flows and one of the mathematical Millennium Prize Problem,187-197, Proc. 8-th Int. Sci. Sc. “ Waves and Vortices in Complex media”, 7-9 Nov, A. Yu. Ishlinskii IPM RAS, Moscow, 2017
  91. S.G. Chefranov, I.I. Mokhov, A.G. Chefranov, The hydrodynamic singular vortex on the sphere and the Dirac monopole, [physics.flu-dyn] 11 Nov 2017
  92. S.G. Chefranov, A.S. Chefranov. The exact solution to the vortex 3-D Euler equation for compressible medium, F. V. Dolzganskii 80-th year Anniversary Int. Conf. “ Actual problems of geophysical hydrodynamics”, A.M. Obukhov IAF RAS, 23 Nov, Moscow , 2017
  93. S.G. Chefranov, A.S. Chefranov, Exact time-dependent solution to the three-dimensional Euler-Helmholtz and Riemann-Hopf equations for vortex flows of a compressible medium, EuroMech/Ercoftac colloquium “ Turbulent Cascades II”, 05.12-07.12, Ecole Centrale de Lyon (Laboratory of Fluid Mechanics and Acoustics), Lyon, 2017
  94. Sergey G. Chefranov, Aleksander G. Chefranov. Hagen-Poiseuille flow linear instability; Cardiometry; No.5; November 2014; p.17-34; DOI:10.12710/cardiometry.2014.5.1734 Available from:
  95. Sergey G. Chefranov. Linear Eсkman friction in the mechanism of the cycloneanticyclone vortex asymmetry and in a new theory of rotating superfluid; Cardiometry; No.4; May 2014; p.46-69; DOI:10.12710/cardiometry.2014.4.4669 Available from:
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