Welcome to my personal webpage

I am a Full Professor at the Applied Mathematics Department (Matemática Aplicada) in the Institute of Mathematics of the Federal University of Rio de Janeiro (Instituto de Matemática/Universidade Federal do Rio de Janeiro - IM/UFRJ), with a PhD degree in Applied Mathematics from the Indiana University, USA.

My background is on Partial Differential Equations, with emphasis in Infinite Dimensional Dynamical Systems, incompressible Navier-Stokes equations, and statistical solutions connected with turbulence.

— Ricardo M. S. Rosa

News

⟩⟩⟩ Teaching: Stochastic Differential Equations + Navier-Stokes Equations

This semester, 2026/1, I am teaching an undergraduate-level course on Stochastic Differential Equations and a graduate-level course on the mathematical analysis of the incompressible Navier-Stokes equations.

⟩⟩⟩ Recently submitted research papers

• "Optimal minimax formula for bounds on ensemble averages of statistically stationary three-dimensional Navier-Stokes flows" (Anne Bronzi, Cecília F. Mondaini, Ricardo M. S. Rosa), arXiv:2606.12825 [math.AP]

• "Energy cascade for cross-shear length scales in free-shear three-dimensional incompressible viscous flows" (Ricardo M. S. Rosa), arXiv:2603.14626 [math.AP]

• "The Effect of Stochasticity in Score-Based Diffusion Sampling: a KL Divergence Analysis" (Bernardo P. Schaeffer, Ricardo M. S. Rosa, Glauco Valle), arxiv:2506.11378 [cs.LG]

• "On the convergence of trajectory statistical solutions" (Anne C. Bronzi, Cecilia F. Mondaini, Ricardo M.S. Rosa), arXiv:2412.02117 [math.AP]

⟩⟩⟩ Recently published research papers

• "Strong order-one convergence of the Euler method for random ordinary differential equations driven by semi-martingale noises" (Peter E. Kloeden, Ricardo M. S. Rosa) ESAIM: Mathematical Modelling and Numerical Analysis, vol. 59 (2025) - DOI:10.1051/m2an/2025087 (arXiv:2306.15418 [math.PR])

• "Regularity of the global attractor for the 2D incompressible Navier-Stokes equations on channel-like domains" (Ricardo M. S. Rosa) Journal of Differential Equations, vol. 435 (2026) (arXiv:2508.01868 [math.AP])

⟩⟩⟩ Slides of recent talks

• Slides of my talk on the strong convergence of the Euler method for random ODEs driven by semi-martingale noises, given at the Seminários de Probabilidade, at IM/UFRJ, in June 2026

• Slides of my talk on optimal minimax bounds for the Navier-Stokes equations, given at our PDE & Analysis seminar, at IM/UFRJ, in June 2025