The Øresund Seminar - Copenhagen 18/6 2024

Information about the Øresund Seminar in Copenhagen 18/6, 2024

We are happy to announce that the next Øresund Seminar will be held in the summer of 2024.
It will this time take place in Copenhagen, at the Department of Mathematical Sciences at University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen.
The lectures will be in the lecture room Auditorium 3, located centrally in the H.C. Ørsted Institute right across the corridor from the mathematics department:
You can follow this link to find your way to the U Copenhagen mathematics department
(an entrance door is found on the northwest side of the MATH building which faces into the campus park in the direction of the August Krogh Building/Zoology Museum - you can get straight to Auditorium 3 (see the exact room location here) by continuing southeast through the main hall from this entry door).

Below is a schedule for the day. After the talks, we will go for dinner.
We need to know before Friday June 14th, at 12 noon (Copenhagen time) if you want to join for dinner.
Please sign up at <https://www.math.ku.dk/english/calendar/events/oeresundsseminaret_june2024> if you want to join for dinner.
(Dinner location, June 18th, 2024: Brasserie Barner, Århusgade 1, 2100 København Ø.)

13.15-14.00: Michele Coti Zelati (Imperial College)

Title: Stability thresholds in three dimensional stratified fluids
Abstract: Click to expand →

Abstract:

The stability of shear flows in the fluid mechanics is an old problem dating back to the famous Reynolds experiments in 1883. The question is to quantify the size of the basin of attraction of equilibria of the Navier-Stokes equations depending on the viscosity parameters, giving rise to the so-called stability threshold. In the case of a three-dimensional homogeneous fluid, it is known that the Couette flow has a stability threshold proportional to the viscosity, and this is sharp in view of a linear instability mechanism known as the lift-up effect. In this talk, I will explain how to exploit stratification (i.e. non-homogeneity in the fluid density) to improve this bound: the coupling between density and velocity gives rise to oscillations, which suppress the lift-effect. This can be captured at the linear level in an explicit manner, and at the nonlinear level by combining sharp energy estimates with suitable dispersive estimates.

14.15-15.00: Nicolas Raymond (Université d'Angers)

Title: Purely magnetic tunnelling between radial magnetic wells
Abstract: Click to expand →

Abstract: This blackboard talk is devoted to the semiclassical spectral analysis of the magnetic Laplacian in two dimensions. Assuming that the magnetic field is positive and has two symmetric radial wells, we establish an accurate tunneling formula, that is a one-term estimate of the spectral gap between the lowest two eigenvalues. This gap is exponentially small when the semiclassical parameter goes to zero, but positive.

Joint work with S. Fournais and L. Morin.

15.00-15.30 Coffee break

15.30-16.15: Gabriele Brüll (Lund University)

Title: Thin fluid films heated from below
Abstract: Click to expand →

Abstract:

Thin liquid films find various applications in industrial processes. These films, ranging from nanometers to micrometers in thickness, are often exposed to temperature gradients, which compete with stabilizing surface tension effects. A mathematical model describing the evolution of thin fluid film's height resting on a horizontal, heated plate can be derived via lubrication approximation, constituting a quasilinear, degenerate, fourth-order partial differential equations.

When a critical temperature disparity between the heated plate and the surrounding environment is reached, the flat steady state becomes spectrally unstable and periodic stationary solutions bifurcate. Using a Hamiltonian formulation of the stationary problem and analytic bifurcation theory, we prove the existence of a global bifurcation curve converging to a weak stationary periodic solution exhibiting film rupture.

This is a joint work with B. Hilder (TU Munich, Germany) and J. Jansen (Lund University, Sweden).

16.30-17.15: Søren Fournais (University of Copenhagen)

Title: The energy of the dilute Bose gas: A simple approach?
Abstract: Click to expand →

Abstract: In this talk, I will present recent progress on the second order correction to the energy of the dilute Bose gas in the thermodynamic limit. By combining the original approach by Fournais and Solovej with recent advances by Haberberger, Hainzl, Nam, Seiringer and Triay on using Neumann bracketing in the localization step, one obtains a much shorter realization of the basic ideas of the original proof.

Information about the Øresund Seminar in Copenhagen 18/6, 2024

13.15-14.00: Michele Coti Zelati (Imperial College)

Title: Stability thresholds in three dimensional stratified fluids
Abstract: Click to expand →

Abstract:

14.15-15.00: Nicolas Raymond (Université d'Angers)

Title: Purely magnetic tunnelling between radial magnetic wells
Abstract: Click to expand →

15.00-15.30 Coffee break

15.30-16.15: Gabriele Brüll (Lund University)

Title: Thin fluid films heated from below
Abstract: Click to expand →

Abstract:

16.30-17.15: Søren Fournais (University of Copenhagen)

Title: The energy of the dilute Bose gas: A simple approach?
Abstract: Click to expand →

This talk is based on joint work with J.P. Solovej and T. Girardot, L. Junge, L. Morin, M. Olivieri and A. Triay.

18.30 Dinner at Brasserie Barner

Information about the Øresund Seminar in Copenhagen 18/6, 2024

13.15-14.00: Michele Coti Zelati (Imperial College)

Title: Stability thresholds in three dimensional stratified fluidsAbstract: Click to expand →

Abstract:

14.15-15.00: Nicolas Raymond (Université d'Angers)

Title: Purely magnetic tunnelling between radial magnetic wells Abstract: Click to expand →

15.00-15.30 Coffee break

15.30-16.15: Gabriele Brüll (Lund University)

Title: Thin fluid films heated from belowAbstract: Click to expand →

Abstract:

16.30-17.15: Søren Fournais (University of Copenhagen)

Title: The energy of the dilute Bose gas: A simple approach?Abstract: Click to expand →

This talk is based on joint work with J.P. Solovej and T. Girardot, L. Junge, L. Morin, M. Olivieri and A. Triay.

18.30 Dinner at Brasserie Barner

Title: Stability thresholds in three dimensional stratified fluids
Abstract: Click to expand →

Title: Purely magnetic tunnelling between radial magnetic wells
Abstract: Click to expand →

Title: Thin fluid films heated from below
Abstract: Click to expand →

Title: The energy of the dilute Bose gas: A simple approach?
Abstract: Click to expand →