3 papers
math.AP2025
Singularidades para as soluções das Equações de Navier-Stokes and Euler e o Problema do Milênio
Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
The purpose of this note is to offer a birds-eye view on the history and the state-of-the-art in the research surrounding the Millenium Prize problem for the Navier-Stokes equation…
math.AP2025
Absence of anomalous dissipation for vortex sheets
Tarek Elgindi, Milton Lopes Filho, Helena Nussenzveig Lopes
A family of solutions of the incompressible Navier-Stokes equations is said to present anomalous dissipation if energy dissipation due to viscosity does not vanish in the limit of…
math.AP2022
The incompressible --Euler equations in the exterior of a vanishing disk
Adriana Valentina Busuioc, Dragos Iftimie, Milton Lopes Filho +1
In this article we consider the --Euler equations in the exterior of a small fixed disk of radius . We assume that the initial potential vorticity is compactly supported and…