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.