## 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)*