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Upcoming talks


Szeftel, Jeremie (UMPC Paris) WPI, OMP 1, Seminar Room 08.135 Mon, 23. Oct 17, 14:00
The nonlinear stability of Schwarzschild
I will discuss a joint work with Sergiu Klainerman on the stability of Schwarzschild as a solution to the Einstein vacuum equations with initial data subject to a certain symmetry class.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Vega, Luis (BCA Bilbao) WPI, OMP 1, Seminar Room 08.135 Mon, 23. Oct 17, 15:30
Selfsimilar solutions of the Binormal Flow: a new approach
I shall present some recent results obtained with F. de la Hoz about the selfsimilar solutions of the Binormal Flow, also known as the Vortex Filament Equation. Some connections with the transfer of energy in the case when the filament is a regular polygon will be also made.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Visciglia, Nicola (U.Pisa) WPI, OMP 1, Seminar Room 08.135 Mon, 23. Oct 17, 16:30
Large data scattering for gKdV
By combining the Kenig-Merle approach with a suitable inequality proved by Tao we deduce that solutions to gKdV, in the L^2-supercitical regime, scatter to free waves for large times.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Lenzman, Enno (U.Basel) WPI, OMP 1, Seminar Room 08.135 Tue, 24. Oct 17, 9:00
Energy-Critical Half-Wave Maps: Solitons and Lax Pair Structure
We discuss some essential features of solitons for the energy-critical half-wave maps equation. Furthermore, we will present a Lax pair structure and explain its applications to understanding the dynamics. The talk is based on joint work with P. Gérard (Orsay) and A. Schikorra (Pittsburgh).
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Munoz, Claudio (U. Chile Santiago) WPI, OMP 1, Seminar Room 08.135 Tue, 24. Oct 17, 10:30
Local decay estimates for nonlinear equations in the energy space
In this talk we will discuss some recent improvements on well-known decay estimates for nonlinear dispersive and wave equations in 1D with supercritical decay, or no decay at all. Using Virial estimates, we will get local decay where standard dispersive techniques are not available yet. These are joint works with M.-A. Alejo, M. Kowalczyk, Y. Martel, F. Poblete, and J.-C. Pozo.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Merle, Frank (IHES & U. Cergy Pontoise) WPI, OMP 1, Seminar Room 08.135 Tue, 24. Oct 17, 15:00
Different notion of nondispersive solutions for hyperbolic problems
We will see various notion of nondispersive solution in the case of the energy criticl wave equation and applications.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Lan, Yang (U.Basel) WPI, OMP 1, Seminar Room 08.135 Tue, 24. Oct 17, 16:30
On asymptotic dynamics for $L^2$-critical gKdV with saturated perturbations
We consider the $L^2$ critical gKdV equation with a saturated perturbation. In this case, all $H^1$ solution are global in time. Our goal is to classify the asymptotic dynamics for solutions with initial data near the ground state. Together with a suitable decay assumption, there are only three possibilities: (i) the solution converges asymptotically to a solitary wave, whose $H^1$ norm is of size $gamma^{-2/(q-1)}$, as $gammarightarrow0$; (ii) the solution is always in a small neighborhood of the modulated family of solitary waves, but blows down at $+infty$; (iii) the solution leaves any small neighborhood of the modulated family of the solitary waves. This extends the result of classification of the rigidity dynamics near the ground state for the unperturbed $L^2$ critical gKdV (corresponding to $gamma=0$) by Martel, Merle and Rapha"el. It also provides a way to consider the continuation properties after blow-up time for $L^2$ -crtitical gKdV equations.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Zaag, Hatem (U.Paris 13) WPI, OMP 1, Seminar Room 08.135 Wed, 25. Oct 17, 9:00
Blow-up solutions for two non-variational semilinear parabolic systems
We consider two non-variational semilinear parabolic systems, with different diffusion constants between the two components. The reaction terms are of power type in the first system. They are of exponential type in the second. Using a formal approach, we derive blow-up profiles for those systems. Then, linearizing around those profiles, we give the rigorous proof, which relies on the two-step classical method: (i) the reduction of the problem to a finite-dimensional one, then, (ii) the proof of the latter thanks to Brouwer's lemma. In comparison with the standard semilinear heat equation, several technical problems arise here, and new ideas are needed to overcome them. This is a joint work with T. Ghoul and V.T. Nguyen from NYU Abu Dhabi.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Collot, Charles (U.Nice) WPI, OMP 1, Seminar Room 08.135 Wed, 25. Oct 17, 10:30
Shock formation for Burgers equation with transversal viscosity
This talk is about singularity formation for solutions to $$ (*) partial_{t}u+upa_x u-pa_{yy}u=0, (x,y) in mathbb R^2 $$ which is a simplified model of Prandtl's boundary layer equation. Note that it reduces to Burgers equation for $y$-independent solutions $u(t,x,y)=v(t,x)$. We will first recast the well-known shock formation theory for Burgers equation using the framework of self-similar blow-up. This will provide us with an analytic framework to study the effect of the transversal viscosity. The main result (still work in progress) is the construction and precise description of singular solutions to $(*)$. This is joint work with T.E. Ghoul and N. Masmoudi.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Banica, Valeria (U.Evry) WPI, OMP 1, Seminar Room 08.135 Wed, 25. Oct 17, 15:00
1-D cubic NLS with several Diracs as initial data and consequences
We solve the cubic nonlinear Schrödinger equation on $mathbb R$ with initial data a sum of Diracs. Then we describe some consequences for a class of singular solutions of the binormal flow, that is used as a model for the vortex filaments dynamics in 3-D fluids and superfluids. This is a joint work with Luis Vega.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Ivanovici, Oana (CNRS Nice) WPI, OMP 1, Seminar Room 08.135 Wed, 25. Oct 17, 16:30
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Talks of the past month


Michael Kniely Seminar Room 08.135 Wed, 18. Oct 17, 0:00
On two problems in the field of semiconductor materials and photovoltaics
The first part of the talk is concerned with a semiconductor model including trapped states in an intermediate energy band. We will introduce a reaction-drift-diffusion system and employ the entropy approach in order to obtain an entropy-entropy production (EEP) inequality. In particular, we shall focus on the derivation of the EEP-inequality. Exponential convergence to the equilibrium is then a consequence of this EEP-estimate. An interesting feature of our results is the fact that the EEP-constant, and hence the convergence rate, is independent of the average lifetime of an electron in a trapped state. In the second part of the talk, we will investigate a material design problem in the context of photovoltaics. We employ a quantum-mechanical model for a prescribed distribution of positive charges and the corresponding density of negative charges. By a light-induced excitation, the electronic system may end up in an excited state possessing a different electronic structure. Our goal is to maximize the resulting spatial charge transfer as a function of the underlying nuclear charge distribution. A general existence proof regarding an optimal nuclear density as well as numerical results for a chain of atoms will be presented.
  • Thematic program: Mathematical models in Biology and Medicine (2017/2018)

Saut, Jean-Claude WPI, OMP 1, Seminar Room 08.135 Fri, 22. Sep 17, 9:30
Existence of solitary waves for internal waves in two-layers systems
We establish the existence of solitary waves for two classes of two-layers systems modeling the propagation of internal waves. More precisely we consider the Boussinesq-Full dispersion system and the Intermediate Long Wave (ILW) system together with its Benjamin-Ono (B0) limit. This is work in progress with Jaime Angulo Pava (USP)
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on "Recent progress on surface and internal waves models" (2017)

Barros, Ricardo WPI, OMP 1, Seminar Room 08.135 Thu, 21. Sep 17, 14:30
Large amplitude internal waves in three-layer flows
Large amplitude internal waves in a three-layer flow confined between two rigid walls will be examined in this talk. The mathematical model under consideration arises as a particular case of the multi-layer model proposed by Choi (2000) and is an extension of the two-layer MCC (Miyata-Choi-Camassa) model. The model can be derived without imposing any smallness assumption on the wave amplitudes and is well-suited to describe internal waves within a strongly nonlinear regime. We will investigate its solitary-wave solutions and unveil some of their properties by carrying out a critical point analysis of the underlying dynamical system.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on "Recent progress on surface and internal waves models" (2017)

Klein, Christian WPI, OMP 1, Seminar Room 08.135 Thu, 21. Sep 17, 11:00
Numerical study of PDEs with nonlocal dispersion
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on "Recent progress on surface and internal waves models" (2017)

Haspot, Boris WPI, OMP 1, Seminar Room 08.135 Thu, 21. Sep 17, 9:30
Global well-posedness of the Euler-Korteweg system for small irrotational data
The Euler-Korteweg equations are a modification of the Euler equations that takes into account capillary effects. In the general case they form a quasi-linear system that can be recast as a degenerate Schr ̈odinger type equation. Local well-posedness (in subcritical Sobolev spaces) was obtained by Benzoni-Danchin-Descombes in any space dimension, however, except in some special case (semi-linear with particular pressure) no global well- posedness is known. We prove here that under a natural stability condition on the pressure, global well-posedness holds in dimension d ¡Ý 3 for small irrotational initial data. The proof is based on a modified energy estimate, standard dispersive properties if d ¡Ý 5, and a careful study of the nonlinear structure of the quadratic terms in dimension 3 and 4 involving the theory of space time resonance.
  • Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
  • Event: Workshop on "Recent progress on surface and internal waves models" (2017)
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