PDEs in quantum physics, materials and micromagnetism (2017/2018)
Organizers: Sofia Kantorovich (WPI c/o U.Wien), PF Pierre Raphael (U. Nice), PF JeanClaude Saut (U. Paris Sud and ICP), Jörg Schmiedmayer (WPI c/o TU Wien), Dieter Suess (U.Wien), Ulisse Stefanelli (WPI c/o U. Wien), Yong Zhang (Courant and WPI),
OTPF Sabine Andergassen (U. Tübingen)
Talks
Lannes, David 
WPI, OMP 1, Seminar Room 08.135 
Tue, 19. Sep 17, 9:30 
The shoreline problem for the nonlinear shallow water and GreenNaghdi equations 
The nonlinear shallow water equations and the GreenNaghdi equations are the most
commonly used models to describe coastal flows. A natural question is therefore to
investigate their behavior at the shoreline, i.e. when the water depth vanishes. For the
nonlinear shallow water equations, this problem is closely related to the vacuum problem
for compressible Euler equations, recently solved by JangMasmoudi and CoutandShkoller.
For the GreenNaghdi equation, the analysis is of a different nature due to the presence of
linear and nonlinear dispersive terms. We will show in this talk how to address this
problem. 
 Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
 Event: Workshop on "Recent progress on surface and internal waves models" (2017)

Ehrnstrom, Mats 
WPI, OMP 1, Seminar Room 08.135 
Tue, 19. Sep 17, 11:00 
Smallamplitude solitary waves for the fulldispersion KadomtsevPetviashvili equation

Using constrained minimisation and a decomposition in Fourier space, we prove that the KadomtsevPetviashvili (KPI) equation modified with the exact dispersion relation from the gravitycapillary waterwave problem admits a family of small solitary solutions, approximating these of the standard KPI equation. The KPI equation, as well as its fully dispersive counterpart, describes gravitycapillary waves with strong surface tension. This is joint work with Mark Groves, Saarbrücken 
 Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
 Event: Workshop on "Recent progress on surface and internal waves models" (2017)

Duchêne, Vincent 
WPI, OMP 1, Seminar Room 08.135 
Tue, 19. Sep 17, 14:30 
A full dispersion model for the propagation of long gravity waves 
We will motivate and study a model for the propagation of surface gravity waves, which can be viewed as a fully nonlinear bidirectional Whitham equation. This model belongs to a family of systems of GreenNaghdi type with modified frequency dispersion. We will discuss the wellposedness of such systems, as well as the existence of solitary waves.
The talk will be based on a work in collaboration with Samer Israwi and Raafat Talhouk (Beirut) and another in collaboration with Dag Nilsson and Erik Wahlén (Lund) 
 Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
 Event: Workshop on "Recent progress on surface and internal waves models" (2017)

Groves, Mark 
WPI, OMP 1, Seminar Room 08.135 
Wed, 20. Sep 17, 9:30 
Fully localised solitary gravitycapillary water waves (joint work with B. Buffoni and E. Wahlén) 
We consider the classical gravitycapillary waterwave problem in its usual formulation as a threedimensional freeboundary problem for the Euler equations for a perfect fluid. A solitary wave is a solution representing a wave which moves in a fixed direction with constant speed and without change of shape; it is fully localised if its profile decays to the undisturbed state of the water in every horizontal direction. The existence of fully localised solitary waves has been predicted on the basis of simpler model equations, namely the KadomtsevPetviashvili (KP) equation in the case of strong surface tension and the DaveyStewartson (DS) system in the case of weak surface tension. In this talk we confirm the existence of such waves as solutions to the full waterwave problem and give rigorous justification for the use of the model equations. 
 Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
 Event: Workshop on "Recent progress on surface and internal waves models" (2017)

Burtea, Cosmin 
WPI, OMP 1, Seminar Room 08.135 
Wed, 20. Sep 17, 11:00 
Long time existence results for the abcd Bousssinesq systems 
In this talk we will review some long time existence results for the abcdBoussinesq systems. We will discuss both the Sobolev and the nonlocalized, boretype initial data cases. The main idea in order to get a priori estimates is to symmetrize the family of systems of equations verified by the frequencies of magnitude 2^{j} of the unknowns for each j¡Ý0. For the boretype case, an additional decomposition of the initial data into lowhigh frequencies is needed in order to tackle the infiniteenergy aspect of these kind of data. 
 Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
 Event: Workshop on "Recent progress on surface and internal waves models" (2017)

Iguchi, Tatsuo 
WPI, OMP 1, Seminar Room 08.135 
Wed, 20. Sep 17, 14:00 
IsobeKakinuma model for water waves as a higher order shallow water approximation 
We justify rigorously an IsobeKakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom. It is known that the full water wave equations are approximated by the shallow water equations with an error of order $delta^2$, where $delta$ is a small nondimensional parameter defined as the ratio of the typical wavelength to the mean depth. The GreenNaghdi equations are known as higher order approximate equations to the water wave equations with an error of order $delta^4$. In this talk I report that the IsobeKakinuma model is a much higher approximation to the water wave equations with an error of order $delta^6$. 
 Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
 Event: Workshop on "Recent progress on surface and internal waves models" (2017)

Rousset, Frederic 
WPI, OMP 1, Seminar Room 08.135 
Wed, 20. Sep 17, 15:30 
Large time behavior of asymptotic models for waterwaves 
We will discuss modified scattering properties, for small Solutions and/or in the vicinity of a solitary waves for model dispersive equations in dimension one. We will mainly focus on the modified Korteweg de Vries equation and the cubic Nonlinear Schrodinger equation with potential. Joint works with P. Germain and F. Pusateri. 
 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 wellposedness of the EulerKorteweg system for small irrotational data 
The EulerKorteweg equations are a modification of the Euler equations that takes into account capillary effects. In the general case they form a quasilinear system that can be recast as a degenerate Schr ̈odinger type equation. Local wellposedness (in subcritical Sobolev spaces) was obtained by BenzoniDanchinDescombes in any space dimension, however, except in some special case (semilinear with particular pressure) no global well posedness is known. We prove here that under a natural stability condition on the pressure, global wellposedness 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)

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)

Barros, Ricardo 
WPI, OMP 1, Seminar Room 08.135 
Thu, 21. Sep 17, 14:30 
Large amplitude internal waves in threelayer flows 
Large amplitude internal waves in a threelayer flow confined between two rigid walls will be examined in this talk. The mathematical model under consideration arises as a particular case of the multilayer model proposed by Choi (2000) and is an extension of the twolayer MCC (MiyataChoiCamassa) model. The model can be derived without imposing any smallness assumption on the wave amplitudes and is wellsuited to describe internal waves within a strongly nonlinear regime. We will investigate its solitarywave 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)

Saut, JeanClaude 
WPI, OMP 1, Seminar Room 08.135 
Fri, 22. Sep 17, 9:30 
Existence of solitary waves for internal waves in twolayers systems 
We establish the existence of solitary waves for two classes of twolayers systems modeling the propagation of internal waves. More precisely we consider the BoussinesqFull dispersion system and the Intermediate Long Wave (ILW) system together with its BenjaminOno (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)

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 KenigMerle approach with a suitable inequality proved by Tao we deduce that solutions to gKdV, in the L^2supercitical 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 
EnergyCritical HalfWave Maps: Solitons and Lax Pair Structure 
We discuss some essential features of solitons for the energycritical halfwave 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 wellknown 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 $gamma^{2/(q1)}$, 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 blowup 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 
Blowup solutions for two nonvariational semilinear parabolic systems 
We consider two nonvariational 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 blowup profiles for those systems. Then, linearizing around those profiles, we give the rigorous proof, which relies on the twostep classical method: (i) the reduction of the problem to a finitedimensional 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
$$ (*) partial_{t}u+upa_x upa_{yy}u=0, (x,y) in mathbb R^2 $$
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 wellknown shock formation theory for Burgers equation using the framework of selfsimilar blowup. 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 
1D 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 3D 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 
Dispersion estimates for the wave equation outside a strictly convex obstacle in 3D 
We consider the linear wave equation outside a compact, strictly convex obstacle in R^3 with smooth boundary and we show that the linear wave flow satisfies the dispersive estimates as in R^3 (which is not necessarily the case in higher dimensions). 
 Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
 Event: Workshop on „Propagation of Singularities in Dispersive PDEs“ (2017)

Fernández–Pacheco, Amalio (Cavendish Lab, Cambridge) 
ErnstMachHS, 2. Stock Fak. Physik, Strudlhofgasse 4/Boltzmanngasse 5 
Mon, 29. Jan 18, 16:00 
"Investigation of threedimensional magnetic nanostructures for applications in spintronics" 
In this talk, I will show our recent work on 3D magnetic nanostructures for applications in spintronics. We are developing 3D nanoprinting methods based on focused electron beams [2]. In particular, we have achieved great control over the growth of 3D magnetic nanowires for domain wall studies [3]. Advanced magnetic microscopy experiments reveal the magnetic state and magnetisation reversal mechanism of the wires, dominated by their geometry and metallic composition [4]. Recent results also show how controllable domain wall motion along the whole space becomes now possible [5]. This has been realised by development of new methods for 3D nanoprinting and magnetooptical detection of 3D nanostructures.
During the talk, I will discuss novel methodologies to characterise 3D nanomagnets, including magnetooptical, electron and Xray microscopy. I will also highlight key challenges and opportunities of 3D nanomagnetism. 
 Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)

Fritz R.S. Diorico (TU Wien) 
WPI, OMP 1, Seminar Room 08.135 
Fri, 23. Feb 18, 10:00 
Articial Gauge Fields in Quantum Systems 
In this talk, I will present an overview/review of progress in articial gauge fields in quantum systems. I will start with the underlying first principles with the seminal paper of Berry, the Berry or Geometric phase. Following a few month after its publication Wilczek and Zee concluded with Berry's results, that nonAbelian gauges fields can naturally emerge from the adiabatic development of simple quantum systems. I will mainly focus on how ultracold atomic systems can be prepared such that a mapping to a ultracold atoms behaving like charged particles in a magnetic field. The induced gauge field whether abelian or nonAbelian introduces a space dependent coupling between the dressed states of the ultracold atoms. This provides motivation for extending MCTDHX to tackle quantum systems with artificial gauge fields where the spatial dynamics of the dressed states or pseudospins can be studied in great detail. This could open up interesting physics that could potentially be observed in the experiment. 
 Thematic program: PDEs in quantum physics, materials and micromagnetism (2017/2018)
