Time: 3:40-4:30pm Wednesdays
Room: PSA 306
(unless otherwise specified)

Contact:  Svetlana Roudenko - svetlana [at] math.asu.edu

Fall 2006

Spring 2005

Fall 2004

DATE

SPEAKER

TOPIC/ABSTRACT

   February 15

Basil Nicolaenko,
ASU

Title:  New Sufficient Conditions of Local Regularity for Solutions to the 3D Navier-Stokes Equations 

Abstract:  We present a unified approach to derivation of conditions ensuring local regularity of weak solutions to the non-stationary 3D Navier- Stokes equations (NSE). We extend the classical Caffarelli-Kohn- Nirenberg theorem. The latter is formulated in terms of the scaled integral of the velocity gradient; such an integral is invariant with respect to the natural scaling of the NSE. We show that the theorem remains valid if the gradient of the velocity field is replaced by its symmetric or antisymmetric (vorticity) parts. Blow-up methods will be discussed. This is ongoing work with A. Mahalov and G. Seregin (Steklov Inst.) with applications to rotating fluids.            

   February 22
    room : PSA 306

(refreshments at 3pm in PSA 206)

Natasa Pavlovic,
Princeton University
         

Title:  On periodic nonlinear Schr\"{o}dinger equations

Abstract:   In this talk we will present a joint work with Daniela De Silva, Gigliola Staffilani and Nikolaos Tzirakis on global well-posedness for the $L^2$ critical Schr\"{o}dinger equation with periodic boundary conditions in 1D and 2D. By combining an implementation of the method of almost conservation laws with number theoretic techniques we prove that the problem is globally well-posed in 1D in the Sobolev space $H^{s}({\Bbb T})$, for any $s>4/9$ and in 2D in the Sobolev space $H^{s}({\Bbb T}^2)$, for any $s>2/3$.
Our 1D result matches the best known global well-posedness result for the corresponding problem on line. The two dimensional result was already announced by Bourgain while discussing the possible exponent $s$ that the method of almost conservation laws would give in this context. While explicitly writing up the calculations to recover this claim, we noted that in one particular case, a better Strichartz inequality was needed to successfully conclude the argument. We proceed by determining a qualitative $\epsilon$ refined Strichartz type estimate which reduces to counting the lattice points on a "small" portion between two concentric circles.              

   February 23    (Thursday)
time : 3:40-4:30pm

room : PSA 309

 Alex Iosevich,
University of Missouri - Columbia
           

Title:   Spherical averages and lattices points: from Analysis to Number Theory and back...      

Abstract:  We shall discuss a connection between the restriction phenomenon in harmonic analysis and the distribution of lattice points in convex domains in the context to celebrated combinatorial conjecture due to Erdos about the number of distances determined by a finite point set in Euclidean space. Finite field analogs will be mentioned and the problem of affine sub-spaces of quadratic varieties will make a brief appearance.  

   March 1   

Title:  TBA    

Abstract:  TBA 

   March 8   

 
(no meeting)
         

   March 15   

 
Spring Break
         

   March 22   

Lars Diening,
University of Freiburg, Germany  

         

Title:  TBA    

Abstract:  TBA 

   March 29   

Title:  TBA    

Abstract:  TBA