# Recent webinars

## 26/01/2023, Thursday, 16:00–17:00 Europe/Lisbon Online

Andreia Chapouto, University of California, Los Angeles
Disproving the Deift conjecture: the loss of almost periodicity

In 2008, Deift conjectured that almost periodic initial data leads to almost periodic solutions to the Korteweg-de Vries equation (KdV). In this talk, we show that this is not always the case. Namely, we construct almost periodic initial data whose KdV evolution remains bounded but loses almost periodicity at a later time, by building on the new observation that the conjecture fails for the Airy equation. This is joint work with Rowan Killip and Monica Visan

## 19/01/2023, Thursday, 13:30–14:30 Europe/Lisbon Room 6.2.33, Faculty of Sciences of the Universidade de Lisboa — Online

Pasquale Candito, Universidade de Reggio Calabria
Existence results for nonlinear differential problems

The main aim of the talk is to discuss some existence results for nonlinear differential problems. First, a survey on existence results for boundary value problems (Dirichlet, Neumann, Periodic) obtained by using a coincidence point theorem for sequentially continuous mapping, is given. Next, a recent result, established combining a priori bounds, difference, truncations techniques and variational methods, for a two-point boundary value problem, is presented.

## 12/01/2023, Thursday, 13:30–14:30 Europe/Lisbon Online

Jiawei Li, University of Edinburgh
On distributions of random vorticity and velocity fields in turbulent flows

In this talk, we are interested in the vorticity and velocity random fields of turbulent flows. I will introduce the evolution equations for probability density functions of these random fields under some conditions on the flow. I will also talk about several methods we used to solve these PDF PDEs numerically. Based on joint works with Zhongmin Qian and Mingrui Zhou.

## 15/12/2022, Thursday, 13:30–14:30 Europe/Lisbon Room P3.10, Mathematics Building — Online

Ederson Moreira dos Santos, ICMC, Universidade de São Paulo em São Carlos
On Hamiltonian systems with critical Sobolev exponents

In this talk I will report some results about lower order perturbations of the critical Lane-Emden system posed on a bounded smooth domain $\Omega \subset \mathbb{R}^N$, with $N \geq3$, inspired by the classical results of Brézis and Nirenberg of 1993. We solve the problem of finding a positive solution for all dimensions $N \geq 4$. For the critical dimension $N=3$ we show a new phenomenon, not observed for scalar problems. Namely, there are parts on the critical hyperbola where solutions exist for all $1$-homogeneous or subcritical superlinear perturbations and parts where there are no solutions for some of those perturbations.

Ederson-Lisboa-2022.pdf

## 17/11/2022, Thursday, 13:30–14:30 Europe/Lisbon Room P3.10, Mathematics Building — Online

Giuseppe Negro, CAMGSD, Instituto Superior Técnico
Explicit solutions to the cubic wave equation

We construct a two-parameter family of solutions to the focusing cubic wave equation in $\mathbb{R}^{1+3}$. Depending on the values of the parameters, these solutions either scatter to linear ones, blow-up in finite time, or exhibit a new type of unstable behaviour that acts as a threshold between the other two. We further prove that the blow-up behaviour is stable and we characterize the threshold behaviour precisely, both pointwise and in Sobolev sense.

Joint work with Thomas Duyckaerts (Sorbonne Paris Nord).