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