# PDE Seminar Fall 2024

### Fridays, 3:30 — 4:20pm. The talks will be either at the Sony Building or at the Stevenson Center 1 building. See below for the specific building and room of each talk. Occasionally, talks will be virtual via Zoom. When possible, in-person talks will be live streamed.

Date:** Wednesday, Sept 18th (note different day).**

- Speaker:
**Ugo Gianazza, University of Pavia (Italy).** - Title: Moduli of continuity for solutions to degenerate phase transitions.
- Abstract: Click here.
- Location: Sony Building, A1009.

Date:** Friday, Sept 27th.**

- Speaker:
**Kevin Hu, Duke University.** - Title: Small scale creations for 2D free-boundary incompressible Euler equations with surface tension.
- Abstract: In this talk, I will discuss 2D free boundary incompressible Euler equations with surface tension. We construct initial data with a flat free boundary and arbitrarily small velocity, such that the gradient of vorticity grows at least double-exponentially for all times during the lifespan of the corresponding solution. This work generalizes the celebrated result by Kiselev–Šverák to the free boundary setting. The free boundary introduces some major challenges in the proof due to the deformation of the fluid domain and the fact that the velocity field cannot be reconstructed from the vorticity using the Biot-Savart law. We overcome these issues by deriving uniform-in-time control on the free boundary and obtaining pointwise estimates on an approximate Biot-Savart law. This is joint work with Chenyun Luo and Yao Yao.
- Location: Sony Building, A1013.

Date:** Friday, October 18.**

- Speaker:
**Istvan Kadar, Princeton University.** - Title: Construction of multi-soliton solutions for semilinear equations in dimension 3.
- Abstract: The existence of multi black hole solutions in asymptotically flat spacetimes is one of the expectation from the final state conjecture. In this talk, I will present preliminary works in this direction via a semilinear toy model in dimension 3. In particular, I show 1) an algorithm to construct approximate solutions to the energy critical wave equation that converge to a sum of solitons at an arbitrary polynomial rate in (t-r); 2) a robust method to solve the remaining error terms for the nonlinear equation. The methods apply to energy supercritical problems.
- Location: Sony Building, A1013.

Date:** Friday, November 1st.**

- Speaker:
**Misha Perepelitsa, University of Houston.** - Title: TBA.
- Abstract: TBA.
- Location: Sony Building, A1013.

Date:** Friday, November 8.**

- Speaker:
**Lizhe Wan, University of Wisconsin-Madison.** - Title: TBA.
- Abstract: TBA.
- Location: Sony Building, A1013.

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