London PDE Seminar

\( - \partial_t^2 \phi + \Delta \phi = 0 \text{.} \)

The London PDE Seminar is a London-based online seminar featuring speakers at the forefront of mathematical research in partial differential equations.

Upcoming Seminars

The seminar convenes fortnightly, on approximately every other Friday. Some talks will be held in-person, while others will be held on Zoom.

Date/Time: 11:00 (UK time), Friday, 17 June 2022

Location: UCL (in-person)
Room: B20 (Jevons Lecture Theatre), Drayton House, Gordon Street

Speaker: Renato Velozo (University of Cambridge)

Title: Stability of Schwarzschild for the spherically symmetric Einstein-massless Vlasov system

Abstract: The Einstein-massless Vlasov system is a relevant model in the study of collisionless many-particle systems in general relativity. In this talk, I will present a stability result for the exterior of Schwarzschild spacetime as a solution of this system assuming spherical symmetry. We exploit the normal hyperbolicity of the null geodesic flow in a neighborhood of the trapped set, to obtain decay estimates for the stress energy momentum tensor. The main result requires a precise understanding of radial derivatives of the energy momentum tensor, which we estimate using Jacobi fields on the tangent bundle in terms of the Sasaki metric.

Date/Time: 14:00 (UK time), Friday, 17 June 2022

Location: UCL (in-person)
Room: Maths 500, 25 Gordon Street

Speaker: Sameer Iyer (University of California, Davis)

Title: Reversal in the stationary Prandtl equations

Abstract: We discuss a recent result in which we investigate reversal and recirculation for the stationary Prandtl equations. Reversal describes the solution after the Goldstein singularity, and is characterized by spatio-temporal regions in which \(u > 0\) and \(u < 0\). The classical point of view of regarding the Prandtl equations as an evolution \(x\) completely breaks down. Instead, we view the problem as a quasilinear, mixed-type, free-boundary problem. Joint work with Nader Masmoudi.