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Autumn Semester 2023

Date / Time Speaker Title Location
28 September 2023
16:15-18:00 		Jaemin Park
University of Basel
Event Details

PDE and Mathematical Physics

Title Small scale creation for the 2D Boussinesq Equations
Speaker, Affiliation Jaemin Park, University of Basel
Date, Time 28 September 2023, 16:15-18:00
Location HG G 19.2
Abstract In this presentation, we will examine the long-term behaviors of the two- imensional incompressible Boussinesq equations without thermal diffusion. While the Boussinesq equations exhibit energy conservation, the flow's small-scale creation may induce the growth of finer norms in the solutions over time. During this talk, we will construct smooth initial data to demonstrate such norm growth phenomena, both with and without considering kinematic viscosity. Additionally, we will extend our results to provide an example of temperature patch solutions, the curvature and perimeter of which increase as time progresses. This work is a joint work with A. Kiselev and Y. Yao.
Small scale creation for the 2D Boussinesq Equationsread_more
HG G 19.2
19 October 2023
16:15-18:00 		Dr. Lucas Ertzbischoff
Imperial College
Event Details

PDE and Mathematical Physics

Title On thick spray equations
Speaker, Affiliation Dr. Lucas Ertzbischoff, Imperial College
Date, Time 19 October 2023, 16:15-18:00
Location HG G 19.2
Abstract We consider a coupled system between kinetic and fluid equations, describing a cloud of particles immersed within a gas. In the "thick spray" regime, the volume fraction for the particles is not negligible compared to that of the fluid: it raises many difficulties for the study of such system, which seems to present losses of derivatives. In particular, and contrary to some other fluid-kinetic couplings, its mathematical study has almost remained absent. I will review some recent progress on thick spray equations, and show that one can actually build a Cauchy theory in Sobolev regularity (at least for a compressible viscous fluid) when the initial data satisfies a Penrose type stability condition (being in fact necessary and sufficient for well-posedness). This is based on joint works with Aymeric Baradat (CNRS, Université Lyon 1) and Daniel Han-Kwan (CNRS, Nantes Université).
On thick spray equationsread_more
HG G 19.2
26 October 2023
16:15-18:00 		Dr. Michele Dolce
EPFL
Event Details

PDE and Mathematical Physics

Title Stability threshold of the 2D Couette flow in a homogeneous magnetic field
Speaker, Affiliation Dr. Michele Dolce, EPFL
Date, Time 26 October 2023, 16:15-18:00
Location HG G 19.2
Abstract A planar incompressible and electrically conducting fluid can be described by the 2D Navier-Stokes-MHD system. One simple yet physically relevant laminar state is the Couette flow with a constant homogeneous magnetic field, given by \(u_E=(y,0)\), \(B_E=(b,0)\) in the domain \(\mathbb{T}\times\mathbb{R}\). The goal is to estimate how large can be a perturbation of this state while still resulting in a solution close to the laminar regime, thereby preventing the onset of turbulence. We prove that Sobolev regular initial perturbations of size \(O(Re^{-2/3})\), with Re being the Reynolds number, remain close to \(u_E, B_E\) and exhibit dissipation enhancement. The latter quantifies the convergence towards an x-independent state on a time-scale \(O(Re^{-1/3})\), much faster than the standard diffusive one \(O(Re^{-1})\).
Stability threshold of the 2D Couette flow in a homogeneous magnetic fieldread_more
HG G 19.2
9 November 2023
16:15-18:00 		Dr. David Mitrouskas
IST Austria
Event Details

PDE and Mathematical Physics

Title The low-energy spectrum of the strongly coupled polaron
Speaker, Affiliation Dr. David Mitrouskas, IST Austria
Date, Time 9 November 2023, 16:15-18:00
Location HG G 19.2
Abstract The polaron model describes an electron interacting with a polarizable crystal which is modelled by a nonrelativistic continuous quantum field. If the interaction between the electron and the field is strong, it is known that the ground state energy is to leading order given by the ground state energy of the semiclassical polaron model, where the field is treated as a classical variable. In this talk, we give a detailed description of the full low-energy spectrum of the (confined) polaron by providing arbitrarily high corrections to the semiclassical energy. More precisely, we present an asymptotic series expansion for every low-energy eigenvalue in inverse powers of the coupling constant. Towards the end of the talk, we will discuss what is known about the low-energy spectrum of the non-confined translation-invariant polaron, in particular, the existence of excited bound states at fixed total momentum. The talk is based on joint works with M. Brooks, K. Mysliwy and R. Seiringer.
The low-energy spectrum of the strongly coupled polaronread_more
HG G 19.2
23 November 2023
16:15-18:00 		Prof. Dr. Antti Knowles
Section of Mathematics, University of Geneva
Event Details

PDE and Mathematical Physics

Title Euclidean field theories and interacting Bose gases
Speaker, Affiliation Prof. Dr. Antti Knowles, Section of Mathematics, University of Geneva
Date, Time 23 November 2023, 16:15-18:00
Location HG G 43
Abstract Euclidean field theories have been extensively studied in the mathematical literature since the sixties, motivated by high-energy physics and statistical mechanics. Formally, such a theory is given by a Gibbs measure associated with a Euclidean action functional over a space of distributions. In this talk I explain how some such theories arise as high-density limits of interacting Bose gases at positive temperature. This provides a rigorous derivation of them starting from a realistic microscopic model of statistical mechanics. I focus on field theories with a quartic, local or nonlocal, interaction in dimensions <= 3. Owing to the singularity of the Gaussian free field in dimensions higher than one, the interaction is ill-defined and has to be renormalized by infinite mass and energy counterterms. The proof is based on a new functional integral representation of the interacting Bose gas. Based on joint work with Jürg Fröhlich, Benjamin Schlein, and Vedran Sohinger.
Euclidean field theories and interacting Bose gasesread_more
HG G 43
30 November 2023
16:15-18:00 		Prof. Dr. Georgios Moschidis
EPFL
Event Details

PDE and Mathematical Physics

Title Weak turbulence on Schwarzschild-AdS spacetime
Speaker, Affiliation Prof. Dr. Georgios Moschidis, EPFL
Date, Time 30 November 2023, 16:15-18:00
Location HG G 19.2
Abstract ''In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. The simplest example of such behaviour is described by the AdS instability conjecture, put forward by Dafermos and Holzegel in 2006; this conjecture suggests that generic small perturbations of the AdS initial data lead to the formation of trapped surfaces when reflecting boundary conditions are imposed at conformal infinity. However, whether a similar scenario also holds in the more complicated case of the exterior region of an asymptotically AdS black hole spacetime has been the subject of debate. In this talk, we will show that weak turbulence does emerge in the dynamics of a quasilinear toy model for the vacuum Einstein equations on the Schwarzschild-AdS exterior spacetimes for an open and dense set of black hole mass parameters. This is joint work with Christoph Kehle.
Weak turbulence on Schwarzschild-AdS spacetimeread_more
HG G 19.2

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