Oleg I. Bogoyavlenskij


Professor

Office: Jeffery Hall, Rm. 515
Phone: (613) 533-2409
Email: oib@queensu.ca
Research: Symmetries, invariants, integrability, Fluid & gas dynamics, magnetohydrodynamics, topological methods

Degrees & Accolades:

Habilitation Doctor (Landau Institute)
Ph.D. (Steklov Institute)
M.Sc. (Moscow State University)

Research Profile:

My recent works were devoted to the new methods of construction of exact solutions of physically important equations: the Navier - Stokes equations for viscous fluid dynamics, Euler's equations of ideal fluid and gas mechanics and magnetohydrodynamics (MHD) equations. I have discovered an infinite family of new invariants of the axisymmetric Euler's equations and viscous MHD equations and have studied different regimes of dynamics of viscous and ideal fluids. I have developed methods of construction of moduli spaces of vortex and magnetic knots.

I am interested in recruiting graduate students who have some knowledge of fluid and gas mechanics and a good knowledge of computer graphics and numerical methods for solving finite-dimensional dynamical systems.

Most Recent Publications:

  • O. Bogoyavlenskij, (2020) "Invariants of the gas dynamics inside the mushroom clouds"
    Physics of Fluids, V.32(10): 106103, 1-5. (PDF, 443 KB)
  • O. Bogoyavlenskij, (2020) "New exact axisymmetric solutions to the Navier - Stokes equations"
    Zeitschrift Naturforschung A, V.75(1): 29-42. (PDF, 7,233 KB)
  • O. Bogoyavlenskij, (2020) "Exact force-free plasma equilibria with axial and with translational symmetries"
    Zeitschrift Naturforschung A, V.76(6): 705-712. (PDF, 433 KB)
  • O. Bogoyavlenskij, (2019) "Up-down asymmetric exact solutions to the Navier - Stokes equations"
    Physics of Fluids, V.31(12): 123108, 1-12. (PDF, 1,033 KB)
  • O. Bogoyavlenskij, (2019) "Invariants and Conserved Quantities for the Helically Symmetric Flows of an Inviscid Gas and Fluid with Variable Density"
    Zeitschrift Naturforschung A, 74(3): 245-251. (PDF, 643 KB)
  • O. Bogoyavlenskij, (2019) "Safety Factor for Time-Dependent Axisymmetric Flows of Barotropic Gas and Ideal Incompressible Fluid"
    Physics of Fluids 31, 026106 (2019). (PDF, 773 KB)
  • O. Bogoyavlenskij, (2018) "Invariants of the Axisymmetric Flows of an Inviscid Gas and Fluid with Variable Density"
    Zeitschrift Naturforschung A, 73(10): 931-937. (PDF, 1,433 KB)
  • O. Bogoyavlenskij, (2018) "Safety factor for the new exact plasma equilibria"
    Zeitschrift Naturforschung A, 73(12):1096-1115. (PDF, 5,433 KB)
  • O. Bogoyavlenskij, (2018) "Invariants of the axisymmetric plasma flows"
    Zeitschrift Naturforschung A, 73(6): 539-546. (PDF, 833 KB)
  • ​O. Bogoyavlenskij, (2017) "Counterexamples to Moffatt's statements on vortex knots"
    Physical Review E, 95, 043104, 14pp. (PDF, 851 KB)
  • O. Bogoyavlenskij, (2017) "Moduli spaces of vortex knots for an exact fluid flow"
    J. Math. Physics, 58, 013101, 28pp. (PDF, 1.6 MB)
  • O. Bogoyavlenskij, (2017) "Vortex knots for the spheromak fluid flow and their moduli spaces"
    J. Math. Anal. Appl., 450, 21-47. (PDF, 1.6 MB)