Workshop on Nonlinear Dispersive Equations   (July 17 - 24)


Organized by P Gérard and N J Mauser.



This workshop, with about 25 participants, brought together a broad variety of international colleagues working on different aspects of dispersive equations, with some focus on the Schrödinger equation. The format was casual, with a few one-hour lectures a day and ample space for discussions and working groups.


Tuesday, July 17
10:30 Welcome by P Gérard and N J Mauser
11:00 A Komech On attractors of nonlinear Hamiltonian wave equations
14:30 P A Markowich Microlocal numerical analysis of Schrödinger type equations
16:00 A Vasseur Quantum transport in random media
Wednesday, July 18
10:00 P Gérard NLS on compact manifolds: general Strichartz estimates
11:00 J M Delort Global existence for NLS with small Cauchy data
14:30 N Tzvetkov NLS on compact manifolds: improved Strichartz estimates for specific geometries
16:00 Y Lvov Weak turbulence theory: development and novel applications
Abstract:     I will talk about general weak turbulence theory, its history, recent developments, and novel applications to semiconductor lasers, Gross-Pitaevskii equations, and internal waves in the ocean. Seemingly disconnected, these topics are very similar from the weak turbulence theory point of view.
Thursday, July 19
10:00 P Miller Semiclassical focusing NLS
11:00 H P Stimming The Schrödinger-Poisson-Xalpha model
14:30 N J Mauser From Dirac-Maxwell to incompressible Euler: limits
16:00 L Rhyzik Time reversal of waves
Friday, July 20
10:00 C Sparber Wigner functions vs. WKB methods
11:00 B Walther Review of some results for maximal oscillatory integrals
Monday, July 23
11:00 A Belloquid Kinetics models: existence and hydrodynamical limit
Abstract:    The global existence of solutions of kinetic models near an absolute Maxwellian is studied under suitable assumptions and it is proved that, as time tends to infinity, the solution approaches a global Maxwellian. We give some indications concerning the validity of such assumptions. More specifically, the BGK equation is discussed.
14:30 M Goldstein Trace of the monodromy states and localization
16:00 V Imaikin Soliton-like asymptotics of weak wave-particle interaction
Tuesday, July 24
10:00 C Schmeiser Burgers-Poisson: a nonlinear dispersive model problem
11:00 K Zhang Hydrodynamic and quantum-hydrodynamic models