Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
Oleg I. Bogoyavlenskij

Oleg I. Bogoyavlenskij

Title: Professor
Office: Jeffery Hall, Rm. 515
Phone: (613) 533-2409
Email: oib@queensu.ca
Research: Symmetries, invariants, integrability, Fluid & gas dynamics, magnetohydrody-namics, 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, (2019) "New exact axisymmetric solutions to the Navier - Stokes equations"
    Zeitschrift Naturforschung A, Accepted October 27. (PDF, 7,233 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)