Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
Organizers: PF Gilles Lebeau (U.Nice), Ansgar Jüngel (TU Wien),
Oana Ivanovici (CNRS c/o U.Nice), Arno Rauschenbeutel (WPI c/o ATI TU Wien), PF JeanClaude Saut (U. Paris Sud &
ICP), Hans Peter Stimming (WPI c/o U.Wien)
Talks
Mauser, Norbert J (WPI & ICP c/o U. Wien) 
WPI Seminar Room 08.135 
Mon, 3. Aug 15, 14:00 
“Welcome to Vienna, birthplace of Boltzmann, Schrödinger and Pauli” 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Brenier, Yann (CNRS X) 
WPI Seminar Room 08.135 
Mon, 3. Aug 15, 14:15 
"When Madelung comes up...." 
After recalling the remarkable formulation made in 1926 by Erwin Madelung of the Schrödinger equation in terms of fluid mechanics, I will introduce a rational scheme, based on the least action principle and some nonlinear rescaling of the time variable, starting from Euler's equations of isothermal compressible fluids (1755), followed by Fourier's heat conduction equation (1807),
leading to Schrödinger's equation of quantum mechanics (1925).
Finally, I will suggest the application of this scheme to Magnetohydrodynamics.
Madelung, E. (1926). "Eine anschauliche Deutung der Gleichung von Schrödinger". Naturwissenschaften 14 (45): 1004–1004.

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Germain, Pierre (Courant) 
WPI Seminar Room 08.135 
Mon, 3. Aug 15, 15:15 
“On the derivation of the kinetic wave equation” 
The kinetic wave equation is of central importance in the theory of weak turbulence, but no rigorous derivation of it is known. I will show how it can be derived from NLS on the torus with random forcing, in the small nonlinearity / big box limit. This is joint work with Isabelle Gallagher and Zaher Hani. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Golse Francois (X) 
WPI Seminar Room 08.135 
Tue, 4. Aug 15, 10:00 
“On the meanfield and classical limits for the Nbody Schrödinger equation” 
This talk proposes a quantitative convergence estimate for the meanfield limit of the Nbody Schrödinger equation that is uniform in the classical limit.
It is based on a new variant of the Dobrushin approach for the mean field limit in classical mechanics, which avoids the use of particle trajectories and
empirical measures, and has a very natural quantum analogue. (Work in collaboration with C. Mouhot and T. Paul).

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Nier, Francis (U. Paris 13) 
WPI Seminar Room 08.135 
Tue, 4. Aug 15, 11:00 
“Phasespace approach to the bosonic mean field dynamics : a review” 
After recalling old or more recent point of views on bosonic quantum field theory and mean field problems, the series of works in collaboration with Z. Ammari will be summarized. This phasespace presentation implements the old dream of an infinite dimensional microlocal analysis. In particular the mean field dynamics is nothing but a propagation of singularity result in the semiclassical regime. This talk will put the stress on the key issues related with the infinite dimensional setting and on the new results for the mean field problem provided by this approach. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Pawilowski, Boris (U. Wien & U. Rennes) 
WPI Seminar Room 08.135 
Tue, 4. Aug 15, 12:00 
“Mean field limits for discrete NLS: analysis and numerics” 
In my thesis, jointly supervised by N.J. Mauser and F. Nier, we deal with approximations of the timedependent linear many body Schrödinger equation with a two particles interaction potential, by introducing a discrete version of the equation and mean field limits.
We consider the bosonic Fock space in a finite dimensional setting.
Mathematical tools include the reduced density matrices and Wigner measure techniques exploiting the formal analogy to semiclassical limits. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Nguyen, Toan (Penn State) 
WPI Seminar Room 08.135 
Tue, 4. Aug 15, 14:00 
"Grenier's iterative scheme for instability and some new applications" 
"The talk is planned to revisit Grenier's scheme for instability of Euler and Prandtl, introduced in his CPAM2000 paper, and to present some new applications in the instability of generic boundary layers and instability of VlasovMaxwell in the classical limit". 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Gottlieb, Alex (WPI) 
WPI Seminar Room 08.135 
Wed, 5. Aug 15, 10:00 
“Entropy measures for quantum correlation” 
We use quantum Rényi divergences to define "correlation" functionals of manyfermion states (density operators on a Fock space).
The "reference" state for the relative entropy functional is the unique gaugeinvariant quasifree (g.i.q.f.) state with the same 1RDM as the state of interest.
That is, the "correlation" of the state of interest is its Rényi divergence from the uniquely associated g.i.q.f. state.
Correlation functionals defined in this way enjoy the following properties:
(a) they take only nonnegative values, possibly infinity;
(b) they assign the value 0 to all Slater determinant states;
(c) they are monotone with respect to restriction of states;
(d) they are additive over independent subsystems;
and
(e) they are invariant under changes of the 1particle basis (Bogoliubov transformations).
The quantum relative entropy or quantum KullbackLeibler divergence is a special and distinguished member of any family of quantum Rényi divergences (of which there are at least two).
The associated correlation functional, defined using quantum KullbackLeibler divergence, we call "nonfreeness."
Nonfreeness enjoys further appealing properties not shared by related correlation functionals:
(f) the nonfreeness of a state X is the minimum possible value for the entropy of X relative to any g.i.q.f. reference state;
(g) there is a simple formula for a pure state's nonfreeness in terms of it's natural occupation numbers;
and
(h) within the convex set of nfermion states with given 1RDM, the nonfreeness minimizer equals the entropy maximizer, which is the Gibbs canonical (nparticle) state.

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Bardos, Claude (WPI & ICP c/o Paris) 
WPI Seminar Room 08.135 
Wed, 5. Aug 15, 11:00 
“Formal derivation of the Vlasov Boltzmann relation” 
I report on current work with Toan Nguyen and Francois Golse. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Luong, Hung (U. Wien) 
WPI Seminar Room 08.135 
Wed, 5. Aug 15, 12:00 
“On the Cauchy problem of some 2d models on the background of 1d soliton solution of the cubic nonlinear Schrödinger equation" 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Besse, Christophe (U. Toulouse) 
WPI Seminar Room 08.135 
Thu, 6. Aug 15, 10:00 
“Exponential integrators for NLS equations with application to rotating BECs“ 
In this talk, I will present various time integrators for NLS equations when the potentials are time dependent. In this case, the usual time splitting schemes fail. I will introduce exponential RungeKutta scheme and Lawson scheme and present some of their properties.

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Descombes, Stephane (U. Nice) 
WPI Seminar Room 08.135 
Thu, 6. Aug 15, 11:00 
“Exponential operator splitting methods for evolutionary problems and applications to nonlinear Schrödinger equations in the semiclassical regime“ 
In this talk, I investigate the error behaviour of exponential operator splitting methods for nonlinear evolutionary problems. In particular, I will present an exact local error representation that is suitable in the presence of critical parameters. Essential tools in the theoretical analysis including timedependent nonlinear Schrödinger equations in the semiclassical regime as well as parabolic initialboundary value problems with high spatial gradients are an abstract formulation of differential equations on function spaces and the formal calculus of Liederivatives. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Zhang, Yong (WPI c/o U. Wien) 
WPI Seminar Room 08.135 
Thu, 6. Aug 15, 13:30 
“Efficient evaluation of nonlocal potentials: NUFFT and Gaussian Sum Approximations” 
We introduce accurate and efficient methods for nonlocal potentials evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipoledipole potentials. Both methods rely on the same assumption: the density is smooth and fast decaying. The first method,proposed by Jiang, Greengard and Bao, evaluates the potential in spherical/polar coordinates using NonUniform FFT algorithm, where the singularity of the Fourier representation disappears automatically, while the second one is based on a Gaussiansum approximation of the singular convolution kernel and Taylor expansion of the density.
Both methods are accelerated by fast Fourier transforms (FFT). They are accurate (1416 digits), efficient ($O(Nlog N)$ complexity), low in storage, easily adaptable to other different kernels, applicable for anisotropic densities and highly parallelizable.

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Stimming, HansPeter (WPI c/o U. Wien) 
WPI Seminar Room 08.135 
Thu, 6. Aug 15, 14:30 
“Absorbing Boundary Conditions for Schrodinger and Wave equations: PML vs ECS” 
The perfectly matched layers (PML) and exterior complex scaling (ECS) methods for absorbing boundary conditions are analyzed using spectral decomposition. Both methods are derived as analytical continuations of unitary to contractive transformations. We find that the methods are mathematically and numerically distinct: ECS is complex stretching that rotates the operator's spectrum into the complex plane, whereas PML is a complex gauge transform which shifts the spectrum. Consequently, the schemes differ in their timestability. Numerical examples
are given. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Summer school "Around Schrödinger equations" (2015)

Colin, Mathieu (Univ. de Bordeaux) 
WPI, Seminar Room 08.135 
Mon, 28. Sep 15, 14:30 
Solitons in quadratic media 
In this talk, we investigate the properties of solitonic
structures arising in quadratic media. More precisely, we look for
stationary states
in the context of normal or anomalous dispersion regimes, that lead
us to either elliptic or nonelliptic systems and we address the problem
of orbital stability. Finally, we present some numerical experiments
in order to compute localized states for several regimes. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Saut, JeanClaude (Univ. Paris d'Orsay) 
WPI, Seminar Room 08.135 
Mon, 28. Sep 15, 15:30 
Full dispersion water waves
models 
We will survey recent results and open problems on various
nonlocal "full dispersion" models of surface water waves.

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Dumas, Eric (Univ. de Grenoble) 
WPI, Seminar Room 08.135 
Tue, 29. Sep 15, 9:15 
Some variants of the focusing NLS equations
Derivation, justification and open problems 
The usual model of nonlinear optics given by the cubic NLS equation
is too crude to describe large intensity phenomenas such as filamentation,
which modifies the focusing of laser beams.
I shall explain how to derive some more appropriate variants of the NLS
model from Maxwell's equations, using improved approximations of the original
dispersion relation or taking ionization effects into account.
I shall provide rigorous error estimates for the models considered,
and also discuss some open problems related to these modified NLS equations.
This is joint work with David Lannes and Jeremie Szeftel. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Hayashi, Nakao (Osaka Univ.) 
WPI, Seminar Room 08.135 
Tue, 29. Sep 15, 11:15 
Asymptotics of solutions to fourthorder nonlinear Schrödinger equations 
We consider the Cauchy problem for the fourthorder nonlinear
Schrödinger equation with a critical nonlinearity and prove the asymptotic
stability of solutions in the neighborhood of the self similar solutions under the
non zero mass condition and the smallness on the data.

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Hirayama; Hiroyuki (Nagoya Univ.) 
WPI, Seminar Room 08.135 
Tue, 29. Sep 15, 14:15 
Wellposedness for a system of quadratic derivative
nonlinear Schrödinger equations with periodic initial data. 
We consider the Cauchy problem of a system of quadratic
derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin
as a model of laserplasma interaction.
In this talk, we prove the wellposedness of this system for the periodic initial data.
In particular, if the coefficients of Laplacian satisfy some conditions,
then the wellposedness is proved at the scaling critical regularity by using U^2 and V^2 spaces. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Klein, Christian (Univ. de Bourgogne) 
WPI, Seminar Room 08.135 
Wed, 30. Sep 15, 9:15 
Numerical study of fractional nonlinear Schrödinger equations 
Using a Fourier spectral method, we provide a detailed numerical investigation of dispersive Schrödingertype equations involving a fractional Laplacian in an onedimensional case. By an appropriate choice of the dispersive exponent, both mass and energy sub and supercritical regimes can be identified. This allows us to study the possibility of finite time blowup versus global existence, the nature of the blowup, the stability and instability of nonlinear ground states and the longtime dynamics of solutions. The latter is also studied in a semiclassical setting. Moreover, we numerically construct ground state solutions of the fractional nonlinear Schrödinger equation. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Le Coz, Stefan (Univ. De Toulouse) 
WPI, Seminar Room 08.135 
Wed, 30. Sep 15, 10:30 
On a singularly perturbed GrossPitaevskii equation 
We consider the 1D GrossPitaevskii equation perturbed by a Dirac potential. Using a fine analysis of the properties of the linear propagator, we study the wellposedness of the Cauchy Problem in the energy space of functions with modulus 1 at infinity. Then we study existence and stability of the black solitons with a combination of variational and perturbation arguments. This is a joint work with Isabella Ianni and Julien Royer.

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Melinand, Benjamin (Univ. de Bordeaux) 
WPI, Seminar Room 08.135 
Wed, 30. Sep 15, 11:15 
The Proudman resonance 
In this talk, I will explain the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. In order to explain this phenomenon, I will prove a local wellposedness of the water waves equations with a non constant pressure at the surface, taking into account the dependence of small physical parameters. Then, I will justify mathematically the historical work of Proudman. Finally, I will study the linear water waves equations and I will give dispersion estimates in order to extend The Proudman resonance to deeper waters. To complete these asymptotic models, I will show some numerical simulations. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Ohta, Masahito (Science University of Tokyo) 
WPI, Seminar Room 08.135 
Thu, 1. Oct 15, 9:15 
Stability of standing waves for a system of nonlinear Schrodinger equations with cubic nonlinearity 
We consider a system of nonlinear Schrodinger equations with cubic nonlinearity, called a coherently coupled NLS system (CCNLS) in nonlinear optics, in one space dimension. We study orbital stability and instability of standing wave solutions of (CCNLS), and prove similar results to Colin and Ohta (2012) which studies a system of NLS equations with quadratic nonlinearity. This is a joint work with Shotaro Kawahara (Tokyo University of Science). 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Pomponio, Alessio (Politecnico di Bari) 
WPI, Seminar Room 08.135 
Thu, 1. Oct 15, 10:30 
BornInfeld equations in the electrostatic case 
The equation in (BI) appears for instance in the BornInfeld nonlinear electromagnetic
theory: in the electrostatic case it corresponds to the Gauss law in the
classical Maxwell theory and so is the electric potential and is an assigned
extended charge density.
We discuss existence, uniqueness and regularity of the solution of (BI). The
results have been obtained in a joint work with Denis Bonheure and Pietro
d’Avenia. 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Stimming, HansPeter (Univ. Wien) 
WPI, Seminar Room 08.135 
Thu, 1. Oct 15, 11:15 
Nonlocal NLS of derivative type for modeling highly nonlocal optical
nonlinearities 
A new NLS type equation is employed for modeling longrange interactions in nonlinear optics, in a collaboration with experimental physicists. It is of quasilinear type and models fluctuations around a 'continuouswave polariton' which are chosen according to Bogoliubov theory. We present a numerical discretization method and simulation results. Mathematical theory for this equation is work in progress.

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Watanabe, Tatsuya (Kyoto Sangyo University) 
WPI, Seminar Room 08.135 
Fri, 2. Oct 15, 9:15 
Uniqueness and asymptotic behavior of ground states for
quasilinear Schrodinger equations arising in plasma physics 
In this talk, we consider a quasiinear Schrodinger equation
which appears in the study of plasma physics.
We are interested in the uniqueness of ground states without
assuming any restriction on a physical parameter.
We also study asymptotic behavior of ground states as
the parameter goes to zero.

 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)

Texier, Benjamin (Univ. de Paris VII) 
WPI, Seminar Room 08.135 
Fri, 2. Oct 15, 10:30 
Spacetime resonances and highfrequency instabilities in twofluid EulerMaxwell systems 
We show that spacetime resonances induce highfrequency instabilities in the twofluid EulerMaxwell system. This implies in particular that the Zakharov approximation to EulerMaxwell is stable if and only if the group velocity vanishes. The instability proof relies on a shorttime representation formula for the flows of pseudodifferential operators of order zero. This is joint work with Eric Dumas (Grenoble) and Lu Yong (Prague). 
 Thematic program: Blowup and Dispersion in nonlinear Schrödinger and Wave equations (2015/2016)
 Event: Workshop on "Quasilinear and nonlocal nonlinear Schrödinger equations" (2015)
