David Goluskin

My research is in the broad area of 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 the convex optimization technique of semidefinite programming to study dynamical systems, for instance to estimate time averages and other properties of attractors.

Interests

• nonlinear dynamics
• fluid dynamics
• computational methods
• variational methods

Courses

• Fall 2022:
• Spring 2023: MATH 550: Topics in Applied Mathematics 
• Summer 2023:

Selected Publications

• I. Tobasco, D. Goluskin, C. R. Doering. Optimal bounds and extremal trajectories for time averages in dynamical systems. 2017. arXiv
• D. Goluskin. Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system. 2016. arXiv
• 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)
• D. Goluskin, C. R. Doering. Bounds for convection between rough boundaries. J. Fluid Mech. 804, 370-386. 2016. arXiv, JFM
• 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
• 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
• D. Goluskin. Internally heated convection and Rayleigh-Bénard convection. Springer. 2015. arXiv, Springer
• D. Goluskin. Internally heated convection beneath a poor conductor. J. Fluid Mech. 771, 36-56. 2015. arXiv, JFM
• 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
• D. Goluskin, E. A. Spiegel. Convection driven by internal heating. Phys. Lett. A 377, 83-92. 2012. arXiv, PLA