School - Around Vortices: from Continuum to Quantum Mechanics

Thematic Program – Incompressible Fluid Dynamics 

IMPA, Rio de Janeiro, March 12 – 21, 2014 


The aim of this school is to introduce young researchers and researchers from other areas to the different aspects of vortex dynamics and vorticity in fluids, superfluids and superconductors. For this purpose researchers will gathered in several areas of differential equations materials, and computational modeling, with interest in continuous and material science involving vortices or vorticity. This set of themes divides naturally among hydrodynamic models, mainly the equations of Euler and Navier- Incompressible stokes and superconductivity and superfluidity models, especially equations of Ginzburg-Landau and Gross-Pitaevskii. These two thematic strands correspond to two research communities with little concrete interaction, but which together make much use of the most modern techniques in non-linear analysis applying them to problems of great interest physical and practical. Focusing on the importance of vortices as a physical and mathematical phenomenon in both communities, the school sought to explore common interests and possible synergy.



Scientific Committee:

 Leonid Berlyand (Penn State University, EUA)

Manuel del Pino (Universidad de Chile, Chile)

Jair Koiller (FGV)

Milton da Costa Lopes Filho (UFRJ)

Anna Laura Mazzucato (Pennsylvania State University, EUA)

Helena Judith Nussenzveig Lopes (UFRJ)

Edriss Saleh Titi (Weizmann Institute, Israel)


Organizing Committee:

Milton da Costa Lopes Filho (UFRJ)

Jair Koiller (FGV)

Helena Judith Nussenzveig Lopes (UFRJ)



Evelyne Miot (École Polytechnique, France)
Introduction to vortex dynamics in two-dimensional or three-dimensional ncompressible flows.

Jon Chapman (Oxford University, UK)
An introduction to Ginzburg-Landau vortices


Eugene Wayne (Boston University, USA)
Vortex solutions in two dimensional fluid flows.

Lia Bronsard (McMasters University, Canada)
Vortices in Ginzburg-Landau systems.

Plenary Talks:

Paolo Antonelli, Gran Sasso Science Institute, Italy.
Analysis of finite energy weak solutions for a class of systems in Quantum Hydrodynamics

Leonid Berlyand, Penn State University. U.S.A.
Phase Separation of Multiple Ginzburg-Landau Vortices Pinned by Small Holes

Fabrice Bethuel, Paris VI, France
Various problems related to the dynamics of the Gross-Pitaevskii equation

Russel Caflisch, University of California, Los angeles, U.S.A.
The Search for Singularities

Jon Chapman, Oxford University, U.K.
Interaction of spiral waves in the Complex Ginzburg-Landau equation

David Dritschel, University of St. Andrews, Scotland, UK.
Dynamics and equilibrium statistics of point vortex flows on the sphere

Thierry Gallay, Institut Fourier, Université de Grenoble I, France.
Infinite energy solutions of the two-dimensional Navier-Stokes equations

Tiziana Giorgi, New Mexico State University, Las Cruces, U.S.A.
Symmetric vortex solutions for Ginzburg-Landau type models

Dragos Iftimie, Université de Lyon I, France.
Can an obstacle change the large time behavior of a viscous incompressible fluid?

Milton Lopes Filho, Universidade Federal do Rio de Janeiro, Brazil.
On the vortex-wave system

Evelyn Lunasin, Naval Academy, Annapolis, U.S.A.
Image restoration using equations of fluid dynamics

Evelyne Miot, CNRS, Université de Paris-Sud XI, France.
Some examples of dynamics for nearly parallel vortex filaments

Andre Nachbin, IMPA, Rio de Janeiro, Brazil.
A hydrodynamic pilot wave model

Monika Nitsche, University of New Mexico, Albuquerque, U.S.A.
Vortex Shedding and Low Order Models

Étienne Sandier, Université de Paris XII, France.
Logarithmic interaction energy for infinitely many points in the plane, Coulomb gases and weighted Fekete sets

Daniel Spirn, University of Minnesota-Twin Cities, U.S.A.
Vortex liquids and phase transition equations

Valerii Vinokur, Argonne National Lab, U.S.A.
Vortex pinning: static and dynamic effec

Contributed Talks:

Maicon Benvenutti
Global nonlinear stability for some steady solutions of three-dimensional incompressible Euler equations with helical symmetry and in the absence of vor- ticity stretching

Stefanella Boatto
Point-Vortex dynamics on surfaces of revolution

Eleonora Moura
The vortex-wave system with a finite number of vortices as the limit of the Euler-alpha model

Paul Krause
On the influence sampling of unstable flow events

Student Session and Poster:

Oleksandr Iaroshenko (14:00-14:20)
Reduction from full Ginzburg-Landau to harmonic map functional in a circular domain

Matthew Mizuhara (14:20-14:40)
A Ginzburg-Landau Model of Cell Motility

Qingtian Zhang (14:40-15:00)
Uniqueness of conservative weak solution to Camassa-Holm equation via characteristics

Cássio Oishi (Unesp-Presidente Prudente)
Numerical methods for solving high Weissenberg number viscoelastic fluid flows


Postal Address: Instituto Nacional de Matemática Pura e Aplicada 
Estrada Dona Castorina 110, Jardim Botânico
Rio de Janeiro, RJ, CEP 22460-320, Brasil