Department of Mathematics

Search

PDE and mathematical physics

×

Modal title

Modal content

Spring Semester 2023

Date / Time Speaker Title Location
23 February 2023
16:15-18:00 		Dr. Luigi De Rosa
Departement Mathematik und Informatik, Universität Basel
Event Details

PDE and Mathematical Physics

Title Intermittency and lower dimensional dissipation in fully developed turbulence
Speaker, Affiliation Dr. Luigi De Rosa, Departement Mathematik und Informatik, Universität Basel
Date, Time 23 February 2023, 16:15-18:00
Location HG G 19.1
Abstract It is well known that the empirical failure of Kolmogorov theoretical prediction (K41) on the local structures of incompressible turbulent flows fails because of the intermittent nature of the velocity field. Several physical intermittency models have been thus proposed to reconcile K41 to experiments and most of them builds on the observable phenomenon that the nontrivial energy dissipation (zero-th law of turbulence) is not space filling, i.e. it is lower dimensional. In this talk I will discuss a recent work, obtained together with Philip Isett, where we propose a machinery to quantitatively translate dimensionality assumptions on the dissipation into deviations from K41 prediction. The approach is rather geometrical and if time permits I will describe how it connects to much more abstract/general settings.
Intermittency and lower dimensional dissipation in fully developed turbulenceread_more
HG G 19.1
2 March 2023
16:15-18:00 		Massimo Sorella
EPFL
Event Details

PDE and Mathematical Physics

Title Non selection of vanishing viscosity solutions to the advection equation and anomalous dissipation
Speaker, Affiliation Massimo Sorella, EPFL
Date, Time 2 March 2023, 16:15-18:00
Location HG G 19.1
Abstract In this seminar we outline a recent example of a turbulent divergence free velocity field \(u \in C^\alpha ([0,1 ] \times \T^2)\), with \(\alpha < 1\), having the \textit{non-selection} property. The latter is defined as follows: consider the sequence \(\{ \theta_\nu \}_{\nu >0}\) of solutions to the associated advection diffusion equation with viscosity parameter \(\nu>0\) and fixed initial datum \(\theta_{\text{in}} \in C^\infty\). Then, at least two distinct limiting solutions of the advection equation in the weak* topology arise from the sequence \(\{\theta_\nu\}_{\nu >0}\) as \(\nu \to 0\). Finally, we also mention a recent result of anomalous dissipation, at the level of the forced Navier--Stokes equations in the sharp regularity class \(L^3_t C^{1/3-}_x\) based on the previous turbulent} velocity field, which in particular implies the failure of the energy balance in the forced Euler equations. These are joint works with Elia Bru\'e, Maria Colombo, Gianluca Crippa and Camillo De Lellis.
Non selection of vanishing viscosity solutions to the advection equation and anomalous dissipationread_more
HG G 19.1
23 March 2023
16:15-18:00 		Prof. Dr. Thierry Gallay
Université Grenoble Alpes
Event Details

PDE and Mathematical Physics

Title Axisymmetric Vortex Rings at High Reynolds Number
Speaker, Affiliation Prof. Dr. Thierry Gallay, Université Grenoble Alpes
Date, Time 23 March 2023, 16:15-18:00
Location HG G 19.1
Abstract We consider axisymmetric solutions without swirl of the 3D Navier-Stokes equations originating from circular vortex filaments at initial time. In the case of a single filament, we construct an asymptotic expansion of the viscous vortex ring in the high Reynolds number regime, where the kinematic viscosity is small compared to the circulation of the vortex. We then show that the unique solution of the axisymmetric Navier-Stokes equations remains close to our approximation over a long time interval, during which the vortex ring moves along its symmetry axis at a speed that was predicted by Kelvin in 1867. To prove that, we introduce self-similar variables located at the (unknown) position of the ring, and we control the evolution of the perturbations using an energy functional related to Arnold's variational characterization of steady states for the 2D Euler equations. This talk is based on joint work with Vladimir Sverak.
Axisymmetric Vortex Rings at High Reynolds Numberread_more
HG G 19.1
30 March 2023
16:00-17:00 		Angeliki Menegaki
IHES, Université Paris-Saclay
Event Details

PDE and Mathematical Physics

Title Quantitative framework for hydrodynamic limits
Speaker, Affiliation Angeliki Menegaki, IHES, Université Paris-Saclay
Date, Time 30 March 2023, 16:00-17:00
Location HG G 19.1
Abstract We will present a new quantitative approach to the problem of proving hydrodynamic limits from microscopic stochastic particle systems, namely the zero-range and the Ginzburg-Landau process with Kawasaki dynamics, to macroscopic partial differential equations. Our method combines a modulated Wasserstein-distance estimate comparing the law of the stochastic process to the local Gibbs measure, together with stability estimates a la Kruzhkov in weak distance and consistency estimates exploiting the regularity of the limit solution. It is simplified as it avoids the use of the block estimates. This is a joint work with Daniel Marahrens and Clément Mouhot (University of Cambridge).
Quantitative framework for hydrodynamic limitsread_more (CANCELLED)
HG G 19.1
27 April 2023
16:15-18:00 		Prof. Dr. Massimiliano Gubinelli
University of Oxford
Event Details

PDE and Mathematical Physics

Title A stochastic analysis of EQFTs: the forward-backwards equation for Grassmann measures.
Speaker, Affiliation Prof. Dr. Massimiliano Gubinelli, University of Oxford
Date, Time 27 April 2023, 16:15-18:00
Location HG G 19.1
Abstract I will report on a research program to use ideas from stochastic analysis in the context of constructive quantum field theories. Stochastic analysis can be summarized as the study of measures on path space via push-forward from Gaussian measures. The basic example is the Ito map which sends Brownian motion to a Markov diffusion process solution to a stochastic differential equation. Parisi-Wu stochastic quantisation can be understood as a stochastic analysis of an Euclidean quantum field, in the above sense. In this talk I will focus on another way to introduce such an "Ito map" which has connection to the continuous renormalization group a la Polchinski and which uses a forward-backwards stochastic differential equation. In order to be able to give a full non-perturbative construction I will focus on the case of Grassmann measures seen as instances of non-commutative random fields.
A stochastic analysis of EQFTs: the forward-backwards equation for Grassmann measures.read_more
HG G 19.1
4 May 2023
16:15-18:00 		Rita Teixeira da Costa
University of Cambridge
Event Details

PDE and Mathematical Physics

Title The Teukolsky equation in the full subextremal range
Speaker, Affiliation Rita Teixeira da Costa, University of Cambridge
Date, Time 4 May 2023, 16:15-18:00
Location HG G 19.1
Abstract The Teukolsky equation is one of the fundamental equations governing linear gravitational perturbations of the Kerr black hole family as solutions to the vacuum Einstein equations. We show that solutions arising from suitably regular initial data decay inverse polynomially in time. Our proof holds for the entire subextremal range of Kerr black hole parameters, \(\vert a\vert < M\). This is joint work with Yakov Shlapentokh-Rothman (Toronto).
The Teukolsky equation in the full subextremal rangeread_more
HG G 19.1
11 May 2023
16:15-18:00 		Dr. Emanuela Giacomelli
LMU
Event Details

PDE and Mathematical Physics

Title On the low density Fermi gas in three dimensions
Speaker, Affiliation Dr. Emanuela Giacomelli, LMU
Date, Time 11 May 2023, 16:15-18:00
Location HG G 19.1
Abstract In recent decades, the study of many-body systems has been an active area of research in both physics and mathematics. In this talk, we will consider a system of N spin 1/2 interacting fermions confined in a box in the dilute regime, with a particular focus on the correlation energy which is defined as the difference between the ground state energy and that of the free Fermi gas. We will discuss some recent results about a first order asymptotics for the correlation energy in the thermodynamic limit where the number of particles and the size of the box are sent to infinity keeping the density fixed. In particular, we will present a new upper bound for the correlation energy, which is consistent with the well-known Huang-Yang formula from 1957.
On the low density Fermi gas in three dimensionsread_more
HG G 19.1
23 May 2023
16:15-18:00 		Prof. Dr. Didier Smets
Sorbonne Université
Event Details

PDE and Mathematical Physics

Title On the applicability of Doeblin Harris type methods to PDE models with partial diffusion
Speaker, Affiliation Prof. Dr. Didier Smets, Sorbonne Université
Date, Time 23 May 2023, 16:15-18:00
Location HG G 43
Abstract The Doeblin Harris method is a well established tool in the study of long time asymptotics for Markov processes. In recent years, it has gained popularity in the PDE community, while adapting to problems for which more traditional tools such as e.g. entropy methods did not seem directly applicable. In the talk we present a simple PDE model involving partial diffusion for which such a strategy turned up fruitful. Extensions to a wider class of models coming from neurosciences raise some interesting questions related to pointwise lower bounds for Green's functions in situations where Hörmander's iterated bracket condition is not satisfied, at least not everywhere. This is joint and ongoing work with Delphine Salort.
On the applicability of Doeblin Harris type methods to PDE models with partial diffusionread_more
HG G 43

Note: if you want you can subscribe to the iCal/ics Calender.

Archive: SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 SS 20 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10

JavaScript has been disabled in your browser