Welcome to my personal webpage

Ricardo Rosa

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

⟩⟩⟩ Article on optimal estimates for the Navier-Stokes equations publised in a special volume in honnor of Ciprian Foias

My most recent article ("Optimal minimax bounds for time and ensemble averages for the incompressible Navier-Stokes equations"), co-authored with Roger Temam, was published in Pure and Applied Functional Analysis, in a special volume in honnor of Ciprian Foias.

⟩⟩⟩ Stochastic and random ordinary differential equations

Just started teaching a course on theoretical and numerical aspects of stochastic and random ordinary differential equations. First time teaching it. It is gonna be a fun ride. Lecture notes in Portuguese availabe on rmsrosa.github.io/notas_sde.

⟩⟩⟩ ChainPlots.jl

ChainPlots.jl is my latest registered package. Its purpose is to display the topology of neural networks built with FluxML/Flux.jl.

⟩⟩⟩ UnitfulBuckinghamPi.jl Package

UnitfulBuckinghamPi.jl is my first registered Julia package! It is based on the package Unitful.jl. The aim of UnitfulBuckinghamPi.jl is to solve for the adimensional Pi groups in a list of Unitful parameters, according to the Buckingham-Pi Theorem. More information in the blog post Buckingham-Pi Theorem and the UnitfulBuckinghamPi.jl package.

⟩⟩⟩ New blog post

In this new post Computing time average bounds for the Van der Pol oscillator in Julia, I continue the problem discussed in the previous post, by exemplifying the theory with the Van der Pol oscillator. It is illustrative to visualize the behavior of the limit cycle along the surface of the auxiliary function that minimizes the estimate of the time average.

⟩⟩⟩ Blog

I used to have a blog about homebrewing, and I finally decided to revamp the blog here, including Math and coding. Here are the initial Greetings post and the first mathematical post entitled Time average bounds via Sum of Squares.

⟩⟩⟩ Slides of my talk at the ICMC Summer Meeting

Here are the slides of my talk in the Special Session on Fluid Dynamics, at the ICMC Summer Meeting on Differential Equations - Chapter 2021.

⟩⟩⟩ ICMC Summer Meeting on Differential Equations 2021

On February 2, at 3pm, I am scheduled to give a talk in the Special Session on Fluid Dynamics, at the ICMC Summer Meeting on Differential Equations - Chapter 2021. I will address my newest article, written jointly with Roger Temam (Indiana University) and entitled "Optimal minimax bounds for time and ensemble averages of dissipative infinite-dimensional systems with applications to the incompressible Navier-Stokes equations", currently availabe at arxiv.org/abs/2010.06730.