Calendar

Posted August 21, 2025
Last modified October 24, 2025

Applied Analysis Seminar Questions or comments?

Roy Goodman, New Jersey Institute of Technology
Leapfrogging and scattering of point vortices

The interaction among vortices is a key process in fluid motion. The n-vortex problem, which models the movement of a finite number of vortices in a two-dimensional inviscid fluid, has been studied since the late 1800s and remains relevant due to its strong link to quantum fluid dynamics. A foundational document in this area is Walter Gröbli's 1877 doctoral dissertation. We apply modern tools from dynamical systems and Hamiltonian mechanics to several problems arising from this work. First, we study the linear stability and nonlinear dynamics of the so-called leapfrogging orbit of four vortices, utilizing Hamiltonian reductions and a numerical visualization method known as Lagrangian descriptors. Second, we analyze the scattering of vortex dipoles using tools from geometric mechanics. While point vortices are typically modeled as massless particles, the final part of this talk will discuss the impact of endowing each particle with a small mass. Although some of the concepts are technical, the presentation will focus on a series of interesting and informative images and animations.

Event contact: Stephen Shipman

Posted November 4, 2025

Applied Analysis Seminar Questions or comments?

Capacities, weighted norm inequalities, and nonlinear partial differential equations

I will present a survey of trace inequalities for fractional integrals, highlighting the role of capacities associated to Sobolev spaces and their connections to nonlinear potential theory and nonlinear partial differential equations

Event contact: Stephen Shipman, Laura Kurtz