Speakers:  M. Cannone (U. Marne-la-Vallée), E. Grenier (ENS Lyon), D. Iftimie (IRMAR), A. Mazzucato (Yale U.), H. J. Nussenzveig Lopes (UNICAMP), F. Poupaud (U. Nice), E. Tadmor (CSCAMM and U. Maryland).
 

In the recent past powerful analytical techniques have been brought to bear upon classical problems in incompressible fluid dynamics with considerable success. Among the problems which currently generate intense activity are: analytical treatment of boundary layers, strong solutions of the Navier-Stokes equations in spaces with borderline regularity and rigorous analysis of different asymptotic regimes using weak convergence techniques. The purpose of this minisymposium is to present a sample of recent work in this spirit, thereby promoting interaction among interested researchers.
 

Schedule of Talks (on Tuesday, Feb. 11, 2003) :
 

09:00-09:25 - E. Tadmor.

09:30-09:55 - A. Mazzucato.

10:00-10:25 - D. Iftimie.

10:30-10:55 - F. Poupaud.

16:50-17:15 - H. Nussenzveig Lopes.

17:20-17:45 - E. Grenier.

17:50-18:15 - M. Cannone.
 

Titles and Abstracts:
 

1. Marco Cannone (Université de Marne-la-Vallée)

Title: "Smooth and singular solutions to the Navier-Stokes equations"

(this is joint work with G. Karch).

Abstract: "The existence of singular solutions of the incompressible Navier-Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions (includingstationary ones), and a pointwise loss of smoothness for solutions are proved in the same function space of pseudomeasure type."

2. Emmanuel Grenier (ENS-Lyon)

Title: "Some asymptotics models in oceanography"

Abstract: "Oceanography leads to the study of various interesting asymptotic regimes of Navier Stokes equations, or of the Primitive equations. We will present some of these limits together with the underlying mathematical difficulties (boundary layers, wave propagation, stability issues)."

3. Dragos Iftimie (IRMAR, Rennes)

Title: "Large time behavior and stability of low regularity global solutions to the 3D Navier-Stokes equations"

4. Anna Mazzucato (Yale University, USA)

Title: "Mild solutions to the Navier-Stokes equation in Besov-Morrey spaces"

Abstract: "We consider a class of modified Besov spaces based on Morrey spaces. We investigate existence and uniqueness of solutions to the Navier-Stokes equation by means of fixed-point methods and Littlewood-Paley theory up to and including the critical scaling. Bounds on the non-linear part are obtained in terms of paraproduct estimates. In particular, at the critical scaling we compare Besov-Morrey spaces with the space $\text{BMO}^{-1}$ of Koch and Tataru."

5. Helena J. Nussenzveig Lopes (University of Campinas, Brasil)

Title: "Large time behavior of two-dimensional vortex dynamics"

6. Frederic Poupaud (Université de Nice)

Title: "Solutions with vortex points for the 2D incompressible Euler equation"

7. Eitan Tadmor (CSCAMM and University of Maryland, USA)

Title: "On borderline regularity and critical thresholds in Euler dynamics"