UVA Harmonic Analysis & PDEs Seminar, Spring 2017

 

Organizers: Francesco Di Plinio, Yen Do, Aseel Farhat, Zoran Grujic

 

Regular time and location: Tuesdays, 3:30-4:30pm, 317 Kerchof Hall

This semester we meet Mondays 11-11:50 in 317 Kerchof Hall.

 

 

Jan 23, 2017

(Kerchof 326,

11-11:50) 

Organizational meeting 

Jan 30, 2017

 

(Kerchof 326, 11-11:50)

Juraj Foldes (UVA)

 

Title: Entropy, Euler equation, and Variational methods

 

Abstract: Two dimensional turbulent flows for large Reynold's numbers can be approximated by solutions of incompressible Euler's equation. As time increases, the solutions of Euler's equation are increasing their disorder; however, at the same time, they are limited by the existence of infinitely many invariants. Hence, it is natural to assume that the limit profiles are functions which maximize an entropy given the values of conserved quantities. Such solutions are described by methods of Statistical Mechanics and are called maximal entropy solutions. Nevertheless, there is no general agreement in the literature on what is the right notion of the entropy. We will show that on symmetric domains, independently of the choice of entropy, the maximal entropy solutions with small energy respect the geometry of the domain.

This is a joint work with Vladimir Sverak (University of Minnesota). 

Feb 06, 2017

 

(Kerchof 317, 11-11:50)

Aseel Farhat (UVA)

 

Title: Mixing By Incompressible Flows

 

Abstract: We will go over two recent papers on mixing by (1) G. Alberti, G. Crippa and A. Mazzucato and by (2) Y. Yao and A. Zlatos. We will present the two constructions of incompressible flows in L^\infty(W^{1,1}) that r-mixes mean-zero initial data to scale r in O(|log(r)|) time. That is, that the bound in the re-arrangement cost conjecture by Bressan is optimal when p=1.

Feb 08, 2017

 

(Kerchof 326, 1-2pm)

 Aseel Farhat (UVA) 

 

Title: Mixing By Incompressible Flows (part II)

(cancelled, moved to next week, see below)

Feb 13, 2017

(Kerchof 317, 11-12)

  Aseel Farhat (UVA) 

 

Title: Mixing By Incompressible Flows (part II)

Feb 20, 2017

 

Feb 27, 2017

(Kerchof 317, 11-12)

Peter Perry (U Kentucky)

 

Title: Soliton Resolution for the Derivative Nonlinear Schr\"{o}dinger Equation

 

Abstract: This talk reports on joint work with Robert Jenkins, Jiaqi Liu, and Catherine Sulem. The derivative nonlinear Schr\"{o}dinger equation (DNLS) is a dispersive nonlinear PDE in one space and one time dimension which describes the propagation of Alfv\'{e}n waves in plasmas, is known to admit solitary wave solutions, and was shown to be completely integrable by Kaup and Newell. We'll outline a proof using the inverse scattering method that this equation has solutions global in time for generic initial data in a weighted Sobolev space and show that for such data, the solution is asymptotic to the sum of a finite number of solitons plus radiation.

March 06, 2017

Spring Break

March 13, 2017

 

(Kerchof 317, 11-11:50)

Liaosha Xu (UVA)

 

   Titte: Pointwise Multipliers In Weighted BMOs And L log^k L Estimates For Vorticity         

   

   Abstract: 

   In this talk we first review some results in harmonic analysis and a theorem on L log L bound for vorticity by Zachary and Zoran. Then we attempt to generalize the theorem by studying L log^k L bound for the vorticity. The main challenge is to extend the pointwise multiplier theorem and the Log-characterization of BMO for more general weight functions. If time allows, there will also be some intuition behind this generalization, i.e. how this could improve the results in a paper on sub-critical blow-up scenarios for 3D NSE.


March 20, 2017

Jared Whitehead (BYU)


Titte: Convective systems with additive noise


Abstract: 


We investigate some of the mathematical and physical properties of a convective system with additive stochastic noise in the temperature evolution equation.  In particular, we develop a methodology to evaluate the stability of a base conductive state even in the presence of a time-dependent white noise.  This is joint work with Juraj Foldes, Nathan Glatt-Holtz, and Geordie Richards.


March 27, 2017

 

(Kerchof 317, 11-11:50)

Liaosha Xu (UVA)

 

   Titte: Pointwise Multipliers In Weighted BMOs And L log^k L Estimates For Vorticity, part II

April 03, 2017

Armen Shirikyan


Title: TBA


Abstract: TBA


April 10, 2017

 Mark Lewers (UVA)

 

Title: TBA

 

Abstract: TBA

April 17, 2017

 

April 24, 2017

 

(Kerchof 317, 11-11:50)

 

Kelsey Goodin (UVA)

 

Title: TBA

 

Abstract: TBA

 

*indicates different day, time, and/or location

 

 

 

Past Talks (Click here for current semester) 

Fall 2014, Spring 2015, Fall 2015, Spring 2016, Fall 2016 

 

 

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