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.

Interests

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

Courses

• Fall 2024:
• Spring 2025: 听 听
• Summer 2025:

Selected Publications

• 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.
• S. Kazemi, R. Ostilla-M贸nico, D. Goluskin. Transition between boundary-limited scaling and mixing-length scaling of turbulent transport in internally heated convection. Phys. Rev. Lett. 129, 024501. 2022.
• F. Fuentes, D. Goluskin, S. Chernyshenko. Global stability of fluid flows despite transient growth of energy. Phys. Rev. Lett. 128, 204502. 2022.
• B. Wen, D. Goluskin, C. R. Doering. Steady Rayleigh-B茅nard convection between no-slip boundaries. J. Fluid Mech. Rapids 933, R4. 2022.
• D. Goluskin, G. Fantuzzi. Bounds on mean energy in the Kuramoto-Sivashinsky equation computed using semidefinite programming. Nonlinearity 32, 1705-1730. 2019.