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: PDEs and Math Modeling

This semester, 2025/2, I am teaching an undergraduate-level course on Partial Differential Equations and Mathematical Modeling.

⟩⟩⟩ Recent 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) to appear in ESAIM: Mathematical Modelling and Numerical Analysis - 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) to appear in Journal of Differential Equations 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) 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]

⟩⟩⟩ 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.