Departement Mathematik

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PDE and mathematical physics

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Frühjahrssemester 2025

Datum / Zeit Referent:in Titel Ort
6. März 2025
16:15-18:00 		Dr. Victor Navarro-Fernández
Department of Mathematics, Imperial College London
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PDE and Mathematical Physics

Titel Exponential mixing with random cellular flows via hypocoercivity
Referent:in, Affiliation Dr. Victor Navarro-Fernández, Department of Mathematics, Imperial College London
Datum, Zeit 6. März 2025, 16:15-18:00
Ort Y27 H 46
Abstract We study a passive scalar equation on a two-dimensional periodic box, where the advecting velocity field is given by a cellular flow with a randomly moving center. We prove that the passive scalar undergoes mixing at an exponential rate, independent of any underlying diffusivity. Furthermore, we show that the velocity field enhances dissipation, and we establish sharp decay rates that, for large times, are deterministic and remain uniform in the diffusivity constant. Our approach is purely Eulerian and relies on a suitable modification of Villani's hypocoercivity method. This is a joint project with C. Seis (Universität Münster).
Exponential mixing with random cellular flows via hypocoercivityread_more
Y27 H 46
19. März 2025
16:15-18:00 		Prof. Dr. Andras Vasy
Stanford University
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PDE and Mathematical Physics

Titel Spectral theory for Dirac type operators on asymptotically Minkowski spaces and the spectral action principle in Lorentzian signature
Referent:in, Affiliation Prof. Dr. Andras Vasy, Stanford University
Datum, Zeit 19. März 2025, 16:15-18:00
Ort Y27 H 46
Abstract I will discuss a microlocal analysis approach to spectral theory on asymptotically Minkowski spaces both for scalar wave operators and also for Dirac type operators. This in turn gives rise to complex powers of the operators, allowing for the analysis of a spectral zeta function, relating its residues to geometric information. This is joint work with Nguyen Viet Dang and Michal Wrochna. Special time: Wednesday, 16:15 Special room: ETH LFW B3
Spectral theory for Dirac type operators on asymptotically Minkowski spaces and the spectral action principle in Lorentzian signatureread_more
Y27 H 46
20. März 2025
16:15-18:00 		Dr. Ayman Said
CNRS
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PDE and Mathematical Physics

Titel A classification theorem for steady Euler flows
Referent:in, Affiliation Dr. Ayman Said, CNRS
Datum, Zeit 20. März 2025, 16:15-18:00
Ort Y27 H 46
Abstract In this talk I am going to present a recent result in collaboration with Tarek Elgindi, Yupei Huang and Chujing Xie where we show that all analytic steady solutions to the Euler equations in a simply connected domain are either radial or global solution to a semi-linear elliptic equation of the \(\Delta \psi= F(\psi)\).
A classification theorem for steady Euler flowsread_more
Y27 H 46
27. März 2025
16:15-18:00 		Dr. Mitchell Taylor
ETH
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PDE and Mathematical Physics

Titel Sharp well-posedness for the free boundary MHD equations
Referent:in, Affiliation Dr. Mitchell Taylor, ETH
Datum, Zeit 27. März 2025, 16:15-18:00
Ort Y27 H 46
Abstract I will discuss a series of recent works written jointly with M. Ifrim, B. Pineau and D. Tataru where we develop a new \emph{fully Eulerian} approach to free boundary fluid dynamics, obtaining the first sharp well-posedness theorems for the free boundary Euler and MHD equations. Our well-posedness theories include (i) Local well-posedness in the Hadamard sense, i.e., local existence, uniqueness, and the first proof of continuous dependence on the data, all at optimal Sobolev regularity; (ii) Enhanced uniqueness: Our uniqueness result holds at the level of scaling, requiring merely integrability in time of the Lipschitz norm of \((v,B)\) and the \(C^{1,\frac{1}{2}}\) norm of the free surface; (iii) Stability bounds: We construct a nonlinear functional which measures, in a suitable sense, the distance between two solutions (even when defined on different domains) and we show that this distance is propagated by the flow; (iv) Energy estimates: We prove refined, essentially scale invariant energy estimates for solutions, relying on a newly constructed family of elliptic estimates; (v) Continuation criterion: We give the first proof of a sharp continuation criterion in the physically relevant pointwise norms, at the level of scaling. In particular, for the Euler equations we show that solutions can be continued as long as the velocity is in \(L_T^1W^{1,\infty}\), the free surface is in \(L_T^1C^{1,\frac{1}{2}}\) and the surface does not self-intersect; (vi) A novel construction of regular solutions, which was not known at any regularity for MHD.
Sharp well-posedness for the free boundary MHD equationsread_more
Y27 H 46
3. April 2025
16:15-18:00 		Prof. Dr. Annalaura Stingo
Ecole Polytechnique
Details

PDE and Mathematical Physics

Titel Trivial resonances for a system of Klein-Gordon equations and statistical applications
Referent:in, Affiliation Prof. Dr. Annalaura Stingo, Ecole Polytechnique
Datum, Zeit 3. April 2025, 16:15-18:00
Ort Y27 H 46
Abstract In the derivation of the kinetic equation from the cubic NLS, a key feature is the invariance of the Schrödinger equation under the action of U(1), which allows the quasi-resonances of the equation to drive the effective dynamics of the correlations. In this talk, I will give an example of equation that does not enjoy such type of invariance and show that the exact resonances always take precedence over quasi-resonances. As a result, the effective dynamics is not of kinetic type but still nonlinear and non-trivial. I will present the problem, the ideas behind the derivation of the effective dynamics and some elements of the proof. This is based on a soon-to-appear work in collaboration with de Suzzoni (Ecole Polytechnique) and Touati (CNRS and Université de Bordeaux).
Trivial resonances for a system of Klein-Gordon equations and statistical applicationsread_more
Y27 H 46
8. Mai 2025
16:15-18:00 		Prof. Dr. Christian Brennecke
Universität Bonn
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PDE and Mathematical Physics

Titel Title T.B.A.
Referent:in, Affiliation Prof. Dr. Christian Brennecke, Universität Bonn
Datum, Zeit 8. Mai 2025, 16:15-18:00
Ort Y27 H 46
Title T.B.A.
Y27 H 46
15. Mai 2025
16:15-18:00 		Dr. Asbjørn Bækgaard Lauritsen
Paris Dauphine
Details

PDE and Mathematical Physics

Titel Title T.B.A.
Referent:in, Affiliation Dr. Asbjørn Bækgaard Lauritsen, Paris Dauphine
Datum, Zeit 15. Mai 2025, 16:15-18:00
Ort Y27 H 46
Title T.B.A.
Y27 H 46

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