David Goluskin


Associate Professor
Department of Mathematics and Statistics
University of Victoria
Email: goluskin at uvic.ca

My research is in the broad area of applied nonlinear dynamics and incorporates both computation and analysis. Much of my work concerns fluid dynamics, but I also study simpler ordinary and partial differential equations. Recently I have been developing ways to use polynomial optimization to study dynamics, for instance to estimate time averages and other properties of attractors. An old public lecture about the challenges of understanding turbulence can be found here.


PhD Applied Mathematics, Columbia University, 2013
MS Applied Mathematics, Columbia University, 2009
BS Applied Mathematics, University of Colorado Boulder, 2007
BS Aerospace Engineering, University of Colorado Boulder, 2007

Teaching: Fall 2023

MATH 236, Introduction to real analysis
MATH 379, Nonlinear dynamical systems and chaos

Publications (arXiv)

arXiv versions closely reflect published versions.

Journal articles

  1. Q. Wang, D. Goluskin, D. Lohse
    Lifetimes of metastable windy states in two-dimensional Rayleigh—Bénard convection with stress-free boundaries
    J. Fluid Mech. Rapids 976, R2. 2023. arXiv, JFM (open access)

  2. H. Oeri, D. Goluskin
    Convex computation of maximal Lyapunov exponents
    Nonlinearity 36, 5378-5400. 2023. arXiv, Nonlinearity

  3. A. Chernyavsky, J. Bramburger, G. Fantuzzi, D. Goluskin
    Convex relaxations of integral variational problems: pointwise dual relaxation and sum-of-squares optimization
    SIAM J. Opt. 33, 481-512. 2023. arXiv, SIOPT

  4. S. Kazemi, R. Ostilla-Mónico, D. Goluskin
    Transition between boundary-limited scaling and mixing-length scaling of turbulent transport in internally heated convection
    Phys. Rev. Lett. 129, 024501. 2022. arXiv, PRL

  5. F. Fuentes, D. Goluskin, S. Chernyshenko
    Global stability of fluid flows despite transient growth of energy
    Phys. Rev. Lett. 128, 204502. 2022. arXiv, PRL, talk

  6. B. Wen, D. Goluskin, C. R. Doering
    Steady Rayleigh—Bénard convection between no-slip boundaries
    J. Fluid Mech. Rapids 933, R4. 2022. arXiv, JFM (open access), talk

  7. J. P. Parker, D. Goluskin, G. M. Vasil
    A study of the double pendulum using polynomial optimization
    Chaos 31, 103102. 2021. arXiv, Chaos

  8. B. Wen, D. Goluskin, M. LeDuc, G. P. Chini, C. R. Doering
    Steady Rayleigh–Bénard convection between stress-free boundaries
    J. Fluid Mech. Rapids 905, R4. 2020. arXiv, JFM

  9. M. Olson, D. Goluskin, W. W. Schultz, C. R. Doering
    Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization
    Physica D 415, 132748. 2020. arXiv, Physica D

  10. J. J. Bramburger, D. Goluskin
    Minimum wave speeds in monostable reaction–diffusion equations: sharp bounds by polynomial optimization
    Proc. R. Soc. A 476, 20200450. 2020. arXiv, Proc A

  11. G. Fantuzzi, D. Goluskin
    Bounding extreme events in nonlinear dynamics using convex optimization
    SIAM J. Appl. Dyn. Syst. 19, 1823-1864. 2020. arXiv, SIADS

  12. D. Goluskin
    Bounding extrema over global attractors using polynomial optimization
    Nonlinearity 33, 4878-4899. 2020. arXiv, Nonlinearity

  13. D. Goluskin, G. Fantuzzi
    Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming
    Nonlinearity 32, 1705-1730. 2019. arXiv, Nonlinearity

  14. D. Goluskin
    Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system
    J. Nonlinear Sci. 28, 621-651. 2018. arXiv, JNLS

  15. I. Tobasco, D. Goluskin, C. R. Doering
    Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems
    Phys. Lett. A 382, 382-386. 2018. arXiv, PLA

  16. G. Fantuzzi, D. Goluskin, D. Huang, S. I. Chernyshenko
    Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization
    SIAM J. Appl. Dyn. Syst. 15, 1962-1988. 2016. arXiv, SIADS (open access)

  17. D. Goluskin, C. R. Doering
    Bounds for convection between rough boundaries
    J. Fluid Mech. 804, 370-386. 2016. arXiv, JFM

  18. D. Goluskin, E. P. van der Poel
    Penetrative internally heated convection in two and three dimensions
    J. Fluid Mech. Rapids 791, R6. 2016. arXiv, JFM

  19. J. von Hardenberg, D. Goluskin, A. Provenzale, E. A. Spiegel
    Generation of large-scale winds in horizontally anisotropic convection
    Phys. Rev. Lett. 115, 134501. 2015. arXiv, PRL

  20. D. Goluskin
    Internally heated convection beneath a poor conductor
    J. Fluid Mech. 771, 36-56. 2015. arXiv, JFM

  21. D. Goluskin, H. Johnston, G. R. Flierl, E. A. Spiegel
    Convectively driven shear and decreased heat flux
    J. Fluid Mech. 759, 360-385. 2014. arXiv, videos, JFM

  22. D. Goluskin, E. A. Spiegel
    Convection driven by internal heating
    Phys. Lett. A 377, 83-92. 2012. arXiv, PLA


  1. D. Goluskin
    Internally heated convection and Rayleigh–Bénard convection
    Springer. 2016. arXiv, Springer


  1. D. Goluskin
    Who ate whom: population dynamics with age-structured predation
    in WHOI GFD 2010 program of study: swimming and swirling in turbulence. 2010.

Book review

  1. D. Goluskin
    Review of Exploring ODEs. By Lloyd N. Trefethen, Ásgeir Birkisson, and Tobin A. Driscoll
    SIAM Rev. 61, 392-393. 2019.


  1. D. Goluskin
    Zonal flow driven by convection and convection driven by internal heating
    Columbia University. 2013. download