Fields Colloquium/Seminar in Applied Math

The Fields Institute Colloquium/Seminar in Applied Mathematics is a  monthly colloquium series for mathematicians in the areas of applied  mathematics and analysis. The series alternates between colloquium  talks by internationally recognized experts in the field, and less formal,  more specialized seminars.In recent years, the series has featured  applications to diverse areas of science and technology; examples  include super-conductivity, nonlinear wave propagation, optical fiber  communications, and financial modeling. The intent of the series is to  bring together the applied mathematics community on a regular basis,  to present current results in the field, and to strengthen the potential for  communication and collaboration between researchers with common  interests. We meet for one session per month during the academic  year. The organizers welcome suggestions for speakers and topics. 

The Fields Institute also hosts a page about this Colloquium/Seminar series. 

More information can be found at the following link: http://www.fields.utoronto.ca/programs/scientific/09-10/applied_math/

Details

Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion

by Evelyn Lunasin  (www) | University of Michigan
Time: 14:10  (Thursday, Apr. 12, 2012)
Location: Fields Institute, 222 College Street
Abstract:
I will present global existence and uniqueness theorems for the two-dimensional non-diffusive Boussinesq system with viscosity only in the horizontal direction. This work improves the global well-posedness results established recently by R. Danchin and M. Paicu for the Boussinesq system with anisotropic viscosity and zero diffusion. We follow some of their ideas, and in proving the uniqueness result, we have used an alternative approach by writing the transported temperature (density) as $\theta = \triangle\xi$ and adapting the techniques of V. Yudovich (1963) for the 2D incompressible Euler equations. This new approach allows us to establish uniqueness results with fewer assumptions on the initial data for the transported quantity $\theta$. Furthermore, our proof is more elementary in that we do not need to resort to using Littlewood-Paley theory or the paraproduct calculus of J. Bony. This is joint work with Adam Larios and Edriss S. Titi

Details

'Ultimate state'' of two-dimensional Rayleigh-B\'enard convection

by Charles Doering  (www) | University of Michigan
Time: 12:10  (Thursday, Apr. 12, 2012)
Location: Fields Institute, 222 College St
Abstract:
Rayleigh-Benard convection is the buoyancy-driven flow of a fluid heated from below and cooled from above. Heat transport by convection an important physical process for applications in engineering, atmosphere and ocean science, and astrophysics, and it serves as a fundamental paradigm of modern nonlinear dynamics, pattern formation, chaos, and turbulence theory. Determining the transport properties of high Rayleigh number convection turbulent convection remains a grand challenge for experiment, simulation, theory, and analysis. In this talk, after a general survey of the theory and applications of Rayleigh-Benard convection we describe recent results for mathematically rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-Benard convection between stress-free isothermal boundaries derived from the Boussinesq approximation of the Navier-Stokes equations. The bounds on the heat transport scaling challenge some popular theoretical arguments regarding the asymptotic high Rayleigh number convection. This is joint work with Jared Whitehead.

Dates in this series

· Wednesday, Apr. 14, 2010: Denjoy-Schwartz and Hamilton-Jacobi (Albert Fathi)
· Wednesday, May. 26, 2010: New Theories of Imagery and Implications for Image Segmentation (Dr Garry Newsam)
· Wednesday, Jun. 02, 2010: Recovering the electrical conductivity from interior data (Prof. Alex Tamasan )
· Wednesday, Jul. 28, 2010: The classical capacity of a quantum channel (Chris King)
· Friday, Aug. 20, 2010: The Landau-de Gennes theory of nematic liquid crystals: Uniaxiality versus Biaxiality (Apala Majumdar)
· Wednesday, Nov. 10, 2010: Optimal transport and geodesics for H1 metrics on diffeomorphism groups (Boris Khesin)
· Wednesday, Nov. 24, 2010: Discrete Elastic Rods and Viscous Threads (Eitan Grinspun)
· Thursday, Nov. 25, 2010: From Sorcery to Science: how Hollywood Physics impacts the Sciences (Eitan Grinspun)
· Wednesday, Dec. 08, 2010: Introduction to the renormalization group as a rigorous tool in probability theory (Abdelmalek Abdesselam)
· Wednesday, Mar. 16, 2011: Breakdown of Smoothness in the Muskat Problem (Charles Fefferman)
· Wednesday, Apr. 20, 2011: Mixed-mode solutions in the differentially heated rotating annulus (Greg Lewis)
· Wednesday, Apr. 20, 2011: Numerical simulation of Faraday waves (Nicolas Perinet)
· Wednesday, Jun. 01, 2011: Resonances and long time integration of nonlinear Schroedinger equations (Erwan Faou)
· Wednesday, Nov. 23, 2011: A self-dual polar decomposition for vector fields (Nassif Ghoussoub)
· Wednesday, Mar. 21, 2012: Two Existence Problems in Interfacial Fluid Dynamics (David Ambrose)
· Wednesday, Mar. 21, 2012: The Geometry of Light Transport (Christian Lessig)
· Thursday, Apr. 12, 2012: Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion (Evelyn Lunasin)
· Thursday, Apr. 12, 2012: 'Ultimate state'' of two-dimensional Rayleigh-B\'enard convection (Charles Doering)