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.
⟩⟩⟩ Recent research papers
"Energy cascade for cross-shear length scales in free-shear three-dimensional incompressible viscous flows" (Ricardo M. S. Rosa), submitted arXiv:2603.14626 [math.AP]
"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]
"The Effect of Stochasticity in Score-Based Diffusion Sampling: a KL Divergence Analysis" (Bernardo P. Schaeffer, Ricardo M. S. Rosa, Glauco Valle), submitted arXiv:2506.11378 [cs.LG]
"On the convergence of trajectory statistical solutions" (Anne C. Bronzi, Cecilia F. Mondaini, Ricardo M.S. Rosa), submitted arXiv:2412.02117 [math.AP]
⟩⟩⟩ Slides of my talk at our PDE & Analysis seminar at IM/UFRJ - June 2025
Here are the slides of my talk on Optimal minimax bounds for the Navier-Stokes equations.