Time

Lecture 1：July 11，6 pm-7:30pm
Lecture 2：July 14，6 pm-7:30pm
Lecture 3：July 18，6 pm-7:30pm
Lecture 4：July 21 ，6 pm-7:30pm

Abstract

Vortex sheets are flows for which there is an interface across which the velocity has a tangential discontinuity, while the normal component is continuous. Such structures are ubiquitous in incompressible fluid dynamics and their evolution still contains unanswered questions. The evolution of a vortex sheet is modeled by the incompressible Euler equations with vorticity given by a Dirac delta supported on a curve or surface. Alternatively, a Lagrangian or explicit description is given by the Birkhoff-Rott equations. I will discuss the well-posedness of these models, focusing mainly on the Euler equations, the ensuing mathematical analysis and some applications, and, time permitting, the wild solutions of the vortex sheet problem.

Biography

Professor Helena Judith Nussenzveig Lopes is an internationally recognized mathematician with numerous notable accomplishments. She is a leading expert on the analysis of PDEs arising in fluid dynamics. Professor Lopes is the recipient of several honors, including an invitation to speak at the 2018 International Congress of Mathematicians (ICM), membership to the Brazilian Academy of Sciences, fellowship to the American Mathematical Society (AMS Fellow), and fellowship to the Society for Industrial and Applied Mathematics (SIAM Fellow). She is currently a full professor at the Federal University of Rio de Janeiro (UFRJ).